THE NEED for supporting multimedia applications in

IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 4, NO. 6, NOVEMBER 2005 2777 Transmission of Adaptive MPEG Video Over Time-Varying Wireess Channes: Modeing and Performance Evauation Laura Gauccio, Giacomo Morabito, Member, IEEE, and Giovanni Schembra Abstract Wireess channes are characterized by high timevarying bit-error rates (BERs). To cope with this probem, severa adaptive forward-error-correction (AFEC) schemes have been proposed in the iterature. They work ocay at the wireess ink, adding a variabe amount of redundancy to the transmitted data in order to maintain the packet error rate beow an acceptabe eve. However, when such schemes are utiized, the bandwidth offered to the appications changes when channe conditions change. In this paper, the effects of these bandwidth variations are investigated in the case of rea-time Motion Picture Experts Group (MPEG) video transmission. The MPEG encoder is controed in order to adapt its emission rate to the current bandwidth offered by the wireess ink. To this end, the encoding quaity is diminished by the source rate controer when the transmission rate has to be decreased due to an increase in the channe BER, whereas it is improved when the transmission rate can be increased due to a decrease in the channe BER. A Markov-based mode, denoted as SBBP/SBBP/1/K, has been introduced to mode the scenario being considered. The anaytica framework aows evauation of the performance of the system and can be used to optimize the design of a video transmission system for wireess channes, providing the instruments to derive the tradeoff between information corruption in the wireess channe and MPEG video encoding quaity. Index Terms Forward error correction (FEC), Motion Picture Experts Group (MPEG), quaity of service (QoS), switched batch Bernoui process (SBBP), wireess channes. I. INTRODUCTION THE NEED for supporting mutimedia appications in dynamic environments where users are equipped with wireess terminas is one of the most chaenging research topics today. In fact, it is known that wireess channes are characterized by bit-error rates (BERs) that are severa orders of magnitude higher than the corresponding vaues for terrestria networks. Accordingy, data packets may arrive at their destination corrupted, thus becoming useess. To overcome this probem, one of the soutions most widey adopted today is using forward error correction (FEC). FEC agorithms introduce a chosen amount of redundancy: the Manuscript received August 15, 2003; revised September 3, 2004; accepted September 13, 2004. The editor coordinating the review of this paper and approving it for pubication is V. K. Bhargava. The work of L. Gauccio and G. Morabito was supported by Ministero de Istruzione, de Università e dea Ricerca (MIUR) under contract VICOM. The work of G. Schembra was supported by MIUR under contract TANGO. The authors are with the Dipartimento di Ingegneria Informatica e dee Teecomunicazioni (DIIT), University of Catania, 95124 Catania, Itay (e-mai: aura.gauccio@diit.unict.it; giacomo.morabito@diit.unict.it; schembra@ diit.unict.it). Digita Object Identifier 10.1109/TWC.2005.858028 higher the BER, the higher the amount of redundancy introduced. However, in wireess channes, the BER is characterized by high time variabiity: There are periods when channe conditions are good, that is, the BER is ow, and periods when channe conditions are bad, that is, the BER is high. In order to maintain a high eve of resource efficiency whie guaranteeing the information accuracy required by appications, severa adaptive FEC (AFEC) schemes have been introduced in the recent past 1], 2], 6], 7]. According to these schemes, the amount of redundancy at any time depends on the channe conditions being ow if channe conditions are good, and high if channe conditions are bad. One consequence is that AFEC schemes cause variations in the bandwidth offered to user appications, which therefore have to adapt their output rate accordingy. This paper focuses on video appications that are destined to become very common in wireess-communication scenarios. More specificay, the target of the paper is the definition of an anaytica framework for the design of a rea-time Motion Picture Experts Group (MPEG) video transmission system over a wireess ink that appies AFEC to keep the packet corruption probabiity acceptabe, i.e., beow a given threshod. The MPEG encoder uses a rate controer that adapts the output rate by appropriatey setting the quantizer scae parameter (QSP) 8], 12], 29] to foow the bandwidth variations, whie maximizing encoding quaity and stabiity. In order to achieve this target, the rate controer monitors the activity of the frame that is being encoded, its encoding mode, and the number of bytes used to encode the previous frames. Then, it chooses the appropriate QSP in such a way that the transmission buffer at the sender site never saturates, even during periods with ow avaiabe bandwidth. The whoe system can be modeed by an emission process that feeds the transmission buffer. The server of this buffer behaves according to the channe conditions estimated by the adaptive error controer: The serving rate is higher when channe conditions are good and ower when channe conditions are bad. Switched batch Bernoui processes (SBBPs) are used to mode both the MPEG source 4], 15], 17], and the server process of the transmission buffer that coincides with the timevarying bandwidth avaiabe in the wireess channe 20], 24] 28]. Accordingy, an SBBP/SBBP/1/K mode is introduced to describe the whoe system. The anaytica framework proposed in the paper is used to evauate the performance in terms of the distortion introduced 1536-1276/$20.00 2005 IEEE

2778 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 4, NO. 6, NOVEMBER 2005 Fig. 1. Mobie termina system architecture. by the quantization mechanism in the encoding process, which are the oss and mean deay in the transmission buffer, at different target packet error probabiities (s) achieved using AFEC. Resuts obtained in the paper can be used to obtain the best tradeoff between encoding quaity, which requires a high avaiabe bandwidth, and information correctness at the destination, which requires a high eve of redundancy, thus causing bandwidth reduction. The rest of the paper is organized as foows. Section II describes the wireess MPEG transmission system considered in this paper. Section III proposes an anaytica framework of the whoe video transmission system, accounting for both the video source and the transmission channe. Section IV provides a derivation of the performance parameters. Section V appies the anaytica framework to a case study in order to demonstrate the mode s capabiity of providing performance insights for the system design. Finay, Section VI concudes the paper. II. DESCRIPTION OF THE SYSTEM The architecture of the video transmission system in the mobie termina considered in this paper is shown in Fig. 1. The adaptive rate source is an adaptive-rate MPEG video source over a User Datagram Protoco (UDP)/IP protoco suite. The video stream generated by the video source is encoded by the MPEG encoder according to the MPEG video standard 30], 31]. In the MPEG encoding standard, the frame, which corresponds to a singe picture in a video sequence, is the basic dispaying unit. Three encoding modes are avaiabe for each frame: intraframes (I), predictive frames (P), and interpoative frames (B). The basic idea behind MPEG video compression is to remove spatia redundancy within a video frame and tempora redundancy between successive video frames. The encoder output is a deterministic period sequence in which the period is a group of pictures (GoPs) reaized with three types of encoded frames. 1) I frames coded using ony information present in the picture itsef in order to provide potentia random access points in the compressed video sequence. The coding is based on the discrete-cosine transform according to the joint photographic experts group (JPEG) coding technique. 2) P frames coded using a coding agorithm simiar to the one used for I frames, but with the addition of motion compensation with respect to the previous I or P frame (forward prediction). 3) B frames coded with motion compensation with respect to the previous I or P frame, and the next I or P frame, or an interpoation between them (bidirectiona prediction). Typicay, I frames require more bits than P frames, whie B frames have the owest bandwidth requirement. In encoding each frame, it is possibe to tune the number of bits needed to represent the frame and, thus, its quaity, by appropriatey choosing the so-caed QSP. Its vaue can range within the set 1, 31]: 1 being the vaue giving the best encoding quaity but requiring the maximum number of bits to encode the

GALLUCCIO et a.: TRANSMISSION OF ADAPTIVE MPEG VIDEO OVER TIME-VARYING WIRELESS CHANNELS 2779 frame, and 31 being the vaue giving the worst encoding quaity, but requiring the minimum number of bits. The QSP can be dynamicay changed according to the feedback aw impemented by the rate controer in order to achieve a given target. The MPEG encoder emits one frame every seconds, and its output is packetized in the packetizer according to the UDP/IP protoco suite: the packetizer fragments the information fow into bocks of U P bytes 1 ; these bocks constitute the payoads for the UDP, which adds a header of 8 bytes; each UDP packet is then put in the payoad fied of an IP packet. The IP packets are then sent to a transmission buffer whose service rate is time varying and depends on the channe condition estimated by the adaptive error controer, as wi be expained beow. The main target of the rate controer is to avoid buffer saturation, which causes osses and ong deays, whie maximizing the encoding quaity and stabiity. To this end, it chooses the QSP parameter according to a feedback aw monitoring the activity of the frame being encoded, its encoding mode (I, P, or B), and the current number of packets in the transmission buffer. The mode introduced in the paper is so genera that it can be appied whatever the feedback aw. The feedback aw used in the paper was introduced in 4] and 17] and, for the sake of competeness, wi be reported in Section V-A. It has been defined in such a way that a controed number of packets are present in the transmission buffer at the end of each GoP, whie pursuing a constant distortion eve within the GoP. Packets eaving the transmission buffer enter the adaptive error controer. Its main target is to use FEC to partiay sove the probem of wireess-ink unreiabiity. The FEC bock creator divides packets into sets of k bocks. These bocks are given as input to the AFEC encoder and encoded in sets of m bocks, with m k. Ifanysetofk or more bocks beonging to the same packet is received correcty, then the origina packet can be reconstructed propery. Obviousy, the arger the vaue of m, the higher the probabiity that the information can be reconstructed at the receiver station, but the ower the wireess-ink bandwidth avaiabe at the video source. The vaue of m is chosen by the FEC controer in such a way that the, i.e., the probabiity that a packet cannot be reconstructed at the receiver station, is no higher than a target vaue ˆP. Given that wireess channe conditions change dynamicay, AFEC encoding is appied, as proposed in 1], 2], 6], and 7]. This encoding technique requires knowedge of the current BER on the ink. This estimation is performed by the wireess channe estimator. The estimated BER vaue is given as input to the FEC controer, which evauates m so that the requirement on the is satisfied. The vaue of m therefore changes in time and, as a consequence, the avaiabe ink capacity c(t) aso changes in time as c(t) = ] k c (1) m(t) 1 If Rea-Time Protoco (RTP)/Rea-Time Contro Protoco (RTCP) protocos are aso used over the UDP/IP protoco suite, the reated overhead shoud be considered. where c is the capacity (in packets/s) when FEC is not used. At any time, the service rate of the transmission buffer is set equa to c(t). Accordingy, both the MPEG encoder output process and the transmission-buffer service process are stochastic processes, the first depending on the behavior of the source and the rate controer, and the second on the BER behavior of the wireess channe. These processes wi be modeed with two discrete-time SBBP processes Ỹ (n) and Ñ(n), respectivey, as described in detai in Section III. III. SYSTEM MODEL In this section, we derive a discrete-time anaytica mode of the system described in the previous section. We wi set the sot duration equa to the video-frame interva. As a first step, Sections III-B and III-C wi describe the modes of the noncontroed MPEG encoder output and the avaiabe capacity of the channe as SBBPs 9]. Then, the whoe system wi be modeed as an SBBP/SBBP/1/K queueing system in Section III-D, where K is the maximum number of packets the transmission buffer can contain. For the sake of competeness, Section III-A provides a brief outine of SBBP processes. A. Switched Batch Bernoui Processes (SBBPs) An SBBP Y (n) is a discrete-time emission process moduated by an underying Markov chain 9], and represents a specia case of the famiy of the hidden Markov mode processes 19]. Each state of the Markov chain is characterized by an emission probabiity density function (pdf): The SBBP emits data units according to the pdf of the current state of the underying Markov chain. Therefore, the SBBP Y (n) is fuy described by the state space I (Y ) of the underying Markov chain, the maximum number of data units the SBBP can emit in one sot r (Y ) MAX, and the matrix set (Q(Y ),B (Y ) )), where Q (Y ) is the transition probabiity matrix of the underying Markov chain, whie B (Y ) is the emission probabiity matrix whose rows contain the emission pdfs for each state of the underying Markov chain. If we indicate the state of the underying Markov chain in the generic sot n as S (Y ) (n), the generic eements of the matrices Q (Y ) and B (Y ) are defined as foows: } Q (Y ) s Y,s Y ] = Prob S (Y ) (n +1)=s Y S (Y ) (n) =s Y s Y,s Y I (Y ) (2) } B (Y ) s Y,r] = Prob Y (n) =r S (Y ) (n) =s Y s Y I (Y ), r ] 0,r (Y ) MAX. (3) We wi introduce an extension to the meaning of the SBBP to mode not ony a source emission process, but aso a video-sequence activity process, and an avaiabe wireesschanne-capacity process. In the atter cases, we wi indicate them as an activity SBBP and a transmission-channe SBBP, respectivey, and their matrices B (Y ) as the activity

2780 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 4, NO. 6, NOVEMBER 2005 probabiity matrix and the channe-transmission probabiity matrix, respectivey. B. Noncontroed MPEG Source Mode The noncontroed MPEG video source is part of the adaptive-rate source shown in Fig. 1 comprising the video source, the MPEG encoder, and the packetizer. We denote it as noncontroed because we are assuming it works with a constant QSP q not controed by the rate controer. The first step in modeing the whoe video transmission system shown in Fig. 1 is the derivation of the SBBP process Ỹ q (n), modeing the emission of the noncontroed MPEG video source at the packetizer output for each QSP q. This mode was cacuated by the authors in 4] and 17]. Here, for the sake of brevity, we wi refer to those works in order to define the notation. The mode captures two different components: the activity-process behavior and the activity/emission reationships. As input, it takes the first- and second-order statistics of the activity process, and the three functions, one for each encoding mode (I, P, or B), characterizing the activity/emission reationships. The state of the underying Markov process of Ỹ q (n) is a doube variabe, S (Ỹ ) (n) =(S (G) (n),s (F ) (n)), where S (G) (n) I (G) is the state of the underying Markov chain of the activity process G(n), and S (F ) (n) J is the frame to be encoded in the GoP at the sot n. The state set I (G) represents the set of activity eves to be captured. For exampe, according to 5], we have I (G) = Very Low, Low, High, Very High}. Set J, on the other hand, represents the set of frames in GoP and depends on the GoP structure. For exampe, if the movie is encoded with the GoP structure IBBPBB, set J is defined as J = I,B,B,P,B,B}. As demonstrated in 4] and 17], the underying Markov chain of Ỹq(n) is independent of q. Therefore, we wi indicate its transition probabiity matrix as Q (Ỹ ) instead of Q (Ỹq), and set (Q (Ỹ ),B (Ỹq) ), for each q 1, 31], defines the SBBP emission process modeing the output fow of the noncontroed MPEG encoder, when it uses a constant QSP vaue q. C. Service SBBP Mode The target of this section is to derive the SBBP mode of the process Ñ(n), which represents the service process of the transmission buffer when AFEC is empoyed. As said so far, it cosey depends on the amount of redundancy the AFEC encoder introduces to achieve the target maximum ˆP due to the wireess channe. As usua, (e.g., 14], 24], and 26]), we assume that the channe behavior can be described by means of an M-states Markov process. Accordingy, channe statistica behavior can be described by an M M transition probabiity matrix Q and by BER i, the BERs for each state of the process i 1,M]. Thus, the service SBBP mode is represented by the foowing parameters: 1) the maximum number of packets that can be transmitted in a time sot r (Ñ) MAX ; 2) the state space I (Ñ) ; 3) the matrix set (Q (Ñ),B (Ñ) ) containing the transition probabiity matrix and the channe-emission probabiity matrix. Obviousy, the transition probabiity matrix Q (Ñ) of the underying Markov chain of the process Ñ(n) coincides with the channe-transition probabiity matrix Q, as cacuated in 26]. The state space I (Ñ) coincides with the channe state space, i.e., I (Ñ) =1,M]. Instead, in order to derive B (Ñ), we have to cacuate the bandwidth reduction due to the AFEC redundancy for each state i of the channe SBBP. This depends on the BER characterizing the state BER i. The FEC redundancy to be introduced to achieve the target ˆP vaue for the maximum shoud be such that the resuting for any state i of the channe P,i is ower than or equa to the target one, i.e., P,i ˆP. (4) According to the notation introduced in Section II, indicating the size of each bock expressed in bits as R, and assuming that osses introduced by the wireess channe are independent and uniformy distributed within a bock, 2 the, when the channe is in the generic state i, can be cacuated as foows: P,i = m =m k+1 ( ) m (1 P BEP,i ) m (P BEP,i ) (5) where P BEP,i represents the probabiity that a bock is corrupted when the channe is in state i, and can be evauated as foows: P BEP,i =1 (1 BER i ) R. (6) Now, substituting (5) in (4), we can numericay find the minimum vaue of m verifying the inequaity in (4) for each vaue i of the channe state. Let us indicate this vaue as m i. Accordingy, the capacity Ñi (in packets/s), which is actuay avaiabe for the transmission of data to obtain a ower than ˆP in the wireess channe when its state is i, can be cacuated as foows: Ñ i = k m i c (7) where c is the channe capacity when no FEC encoding is appied (in packets/s]). In genera, from (7), we obtain a noninteger vaue for Ñi. However, we can assume that, when the channe state is i, in each sot, the channe is abe to transmit either D i = Ñi packets with a probabiity of p Di =1 (Ñi D i ),or(d i +1) packets with a probabiity of p Di +1 =1 p Di,wherewehave indicated the argest integer no greater than x as x. 2 This assumption is accurate if intereaving is utiized, which is usua in wireess communications 28].

GALLUCCIO et a.: TRANSMISSION OF ADAPTIVE MPEG VIDEO OVER TIME-VARYING WIRELESS CHANNELS 2781 In summary, the emission probabiity matrix of the SBBP modeing the channe is B (Ñ) R MXr(Ñ) MAX ], and its generic eement can be cacuated as foows: B (Ñ)] i,d] = pdi, if d = D i p Di +1, if d = D i +1 0, otherwise where r (Ñ) MAX is the maximum number of packets that can be transmitted in one sot, i.e., r (Ñ) (8) MAX = max D i +1}. (9) i The transition probabiity matrix and the state space, together with the channe-emission probabiity matrix and the maximum number of packets that can be transmitted in one sot defined in (8) and (9), competey characterize the channe SBBP mode. D. Video-Transmission-System Mode The adaptive-rate source pursues a given target by impementing a feedback aw in the rate controer, which cacuates the vaue q of the QSP to be used by the MPEG encoder for each frame. The target of this section is to mode the video transmission system as a whoe, indicated here as Σ. Tothis aim, we use a discrete-time queueing system mode. Let K represent the maximum number of packets that can be contained in the queue of the transmission buffer and its server. The server capacity of this queueing system, that is, the number of packets that can eave the queue at each time sot, is a stochastic process that has been modeed with the channe SBBP process Ñ(n). The input of the queue system is the emission process of the adaptive-rate source, indicated here as Ỹ (n). Therefore, at sot n, the transmission-buffer queue size is incremented by Ỹ (n), and decremented by Ñ(n). Both the input and the output processes can be modeed by means of two SBBP processes, as discussed above, where the sot duration is the frame duration. To mode the queueing system, we assume a ate-arrivasystem-with-immediate-access time diagram 3], 11]: Packets arrive in batches, and can enter the service faciity if it is free, with the possibiity of them being ejected amost instantaneousy. Note that in this mode, a packet service time is counted as the number of sot boundaries from the point of entry to the service faciity up to the packet departure time. Therefore, even though we aow the arriving packet to be ejected amost instantaneousy, its service time is counted as 1, not 0. A compete description of Σ at the nth sot requires a three-dimensiona Markov process, whose state is defined as S (Σ) (n) =(S (Q) (n),s (Ñ) (Y (n),s ) (n)), where: 1) S (Q) (n) 0,K] is the transmission-buffer queue state in the nth sot, i.e., the number of packets in the queue and in the service faciity at the observation instant; 2) S (Ñ) (n) is the state of the underying Markov chain of the channe SBBP Ñ(n); (Y 3) S )(n) is the state of the underying Markov chain of Ỹ (n), which coincides with that of Ỹq(n), for any q 1, 31]. According to the ate-arriva-system-with-immediate-access time diagram, the transmission-buffer state in sot (n +1)can be obtained through the Lindey equation 13] s Q = max min ( s Q + r, K ) d, 0 } (10) where s Q is the transmission-buffer state in the generic sot n, whie r and d are the server capacity and the number of arrivas at sot n +1, respectivey. The channe SBBP Ñ(n), modeed in Section III-C, can be equivaenty characterized through the set of transition probabiity matrices M (Ñ) (d), which are transition probabiity matrices incuding the probabiity that the server capacity is d (in packets/sot). These matrices can be obtained from the parameter set (Q (Ñ),B (Ñ) ) as foows: ] M (Ñ) (d) ] s Ñ,s Ñ Ñ(n +1)=d, Prob = Q (Ñ)] ] s Ñ,s Ñ d } S (Ñ) (n +1)=s S(Ñ) (n) =s Ñ Ñ B (Ñ)] ] s Ñ,d 0,r (N) MAX ]. (11) The adaptive-rate source emission process is modeed by an SBBP whose emission probabiity matrix depends on the transmission-buffer state. In order to mode this process, we use the SBBP modes of the noncontroed MPEG video source described in Section III-B, Ỹq(n), for each q 1, 31]. So, we have a parameter set (Q (Ỹ ),B (Ỹ1),B (Ỹ2),...,B (Ỹ31) ), which represents an SBBP whose transition matrix is Q (Ỹ ), and whose emission process is characterized by a set of emission matrices B (Ỹq) } q=1,2,...,31. Consequenty, at each time sot, the emission of the MPEG video source is characterized by an emission probabiity matrix chosen according to the QSP vaue defined by the feedback aw q = φ(s Q,a,j). More concisey, as in (11), for the channe SBBP, we characterize the emission process of the adaptive-rate source through the set of matrices M (Ỹ ) s (r)}, r 0,r (Ỹ ) MAX ], each Q matrix representing the transition probabiity matrix incuding the probabiity of r packets being emitted when the buffer state is s Q. Accordingy, the generic eement of the matrix M (Ỹ ) s (r) can be obtained from the above parameter set Q (Q (Ỹ ),B (Ỹ1),B (Ỹ2),...,B (Ỹ31) ) as foows: M (Ỹ ) s Q ] (r) (i,j ),(i,j )] = a I (Act) Q (Ỹ )] (i,j ),(i,j )] B ) ] (Ỹq (r) f Act(a i,j ) (12) (i,j ),r]

2782 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 4, NO. 6, NOVEMBER 2005 where the foowing hod: 1) q is the QSP chosen when the frame to be encoded is the j th in the GoP, the activity is a, and the transmissionbuffer state before encoding this frame is s Q.Thevaue of q is determined by the feedback aw = φ( ), i.e., q = φ ( s Q,a,j ). (13) 2) f Act (a i,j ) is the probabiity that the generic frame j in the GoP has an activity a when its activity eve is i. This function, as demonstrated in 15], 16], and 21], is a Gamma pdf, whose mean vaue and variance characterize the video trace. 3) I (Act) is the set of a the possibe activities. Finay, we can mode the video transmission system as a whoe. If we indicate two generic states of the system as s Σ = (s Q,s Ñ,s ) and Ỹ s Σ =(s Q,s Ñ,s ), the generic eement of Ỹ the transition matrix of the video transmission system as a whoe Q (Σ) can be cacuated, due to (11) and (12), as foows: Q (Σ)] ( ) ( )] s Q,s Ñ,s, s Ỹ Q,s Ñ,s Ỹ S (Q) (n +1)=s Q, Prob S (Ñ) (n +1)=s Ñ, S (Ỹ ) (n +1)=s, Ỹ = d (Ñ) r (Ỹ ) MAX MAX d=0 r=0 M (Ỹ ) s Q (r) ] M (Ñ) (d) ] s Ñ,s Ñ ] s Ỹ,s Ỹ S (Q) (n) =s Q, S (Ñ) (n) =s, Ñ S (Ỹ ) (n) =s, Ỹ ] ψ ( s Q,s Q,...,r,d ) (14) where ψ(s Q,s Q,...,r,d) is a Booean condition for the queue state behavior, and is defined as foows: ψ ( s Q,s Q,K,r,d ) = 1, if max min s Q + r, K } d, 0 } = s Q 0, otherwise. (15) Once the matrix Q (Σ) is known, we can cacuate the steadystate probabiity array of the system Σ as the soution of the foowing inear system π (Σ) Q (Σ) = π (Σ) π (Σ) (16) 1 =1 where 1 is a coumn array whose eements are equa to 1, and π (Σ) is the steady-state probabiity array, whose generic eement is π (Σ) (s Q,sÑ,sỸ )] = Prob S (Q) (n) =s Q,S (Ñ) (n) =sñ, } S (Ỹ ) (n) =sỹ. (17) A direct soution of the system in (16) may be difficut since the number of states grows exposivey as the maximum transmission buffer size K increases. Nevertheess, many agorithms, e.g., 10], 18], and 23], enabe us to cacuate the array π (Σ), whie maintaining a inear dependence on K. IV. QUANTIZATION-DISTORTION ANALYSIS In this section, we evauate both the static and time-varying statistics of the quantization distortion, represented by the process PSNR(n). More specificay, we wi quantize the PSNR process with a set of L different eves of distortion, µ 1,µ 2,...,µ L }, each representing an interva of distortion vaues where the quaity perceived by the users can be considered constant. As an exampe, for the movie Evita, from a subjective anaysis obtained with 300 tests, the foowing L =5 eves of distortion were envisaged: µ 1 = 31.2, 34.2] db, µ 2 = 34.2, 35.0] db, µ 3 = 35.0, 36.2] db, µ 4 = 36.2, 38.4] db, and µ 5 = 38.4, 52.1] db. The pdf f PSNR (p) can be easiy cacuated from the transition probabiity matrix and the steady-state probabiity array of the whoe system, which have been derived in (14) and (16), respectivey see (18) at the bottom of the page], where the foowing hod: 1) ψ s Q,a,j ](p) is a Booean condition defined as foows ( ψ s Q,a,j ] (p) = 1, if F (j ) φ ( s Q,a,j )) = p. 0, otherwise (19) 2) F (j ) (q) in (19) is the so-caed distortion curve 5], 17], 22] for the generic frame j, which is the curve inking the average PSNR to the QSP vaue, q, used to encode the frame. Now, in order to cacuate the statistics of the quantized PSNR process, et us define the array γ (ζ) in which the generic eement γ (ζ), for each 1,L], is the QSP range giving a distortion beonging to the th eve for a frame encoded with encoding mode ζ I, P, B}. Of course, by so doing, we assume that a variation of q within the interva γ (ζ) does not cause any appreciabe distortion. From the distortion curves for the movie Evita, we have cacuated the foowing QSP f PSNR (p) Prob PSNR(n) =p} = K K s Q =0 s Ñ I(Ñ) i I (G) j J s Q =0 s Ñ I(Ñ) i I (G) Q (Σ) ( ) s Q,s Ñ,(i,j ), ( s Q,s Ñ,(i,j ) a I (Act) f Act (a i,j ) )] π (Σ) s Q,s Ñ,(i,j ) ] ψ s Q,a,j ] (p) (18)

GALLUCCIO et a.: TRANSMISSION OF ADAPTIVE MPEG VIDEO OVER TIME-VARYING WIRELESS CHANNELS 2783 ranges corresponding to the above distortion eves µ, for each 1, 5]. 1) For I frames: γ (I) = 16, 31], 13, 15], 10, 12], 6, 9], 1, 5]]. 2) For P frames: γ (P) = 15, 31], 13, 14], 10, 12], 6, 9], 1, 5]]. 3) For B frames: γ (B) = 17, 31], 14, 16], 11, 13], 7, 10], 1, 6]]. Let q = φ(s Q,a,j ) be the feedback aw, inking the transmission-buffer state at the beginning of a generic sot n, s Q 0,K], the activity of the frame in the same sot, a I (G), and the position in the GoP of the frame to be encoded, j J, to the QSP to be used to encode the current frame. Moreover, for each a and j,etθ (a,j ) = s Q such that φ(s Q,a,j ) γ (ζ) } be the range of vaues of the transmission-buffer state for which the rate controer chooses QSP vaues beonging to the eve µ, according to the adopted feedback aw. By definition, it foows that a variation of the transmission-buffer state within θ (a,j ) does not cause any appreciabe distortion variation. Let us now cacuate the probabiity that the vaue of the process PSNR(n) is in the generic interva µ, π (PSNR) ], and the pdf f δ (m) of the stochastic variabe δ, representing the duration of the time the process PSNR(n) remains in the generic interva µ without interruption. They are defined as π (PSNR) ] = Prob PSNR(n) µ } (20) and (21), shown at the bottom of the page. The term π (PSNR) ] in (20) can be cacuated from the pdf f PSNR (p) obtained in (18) as foows: π (PSNR) ] = p µ f PSNR (p). (22) In order to cacuate the pdf f δ (m) in (21), et us indicate the matrix containing the one-sot probabiities of transition towards system states in which the distortion eve is µ as Q (Σ) µ. It can be obtained from the transition probabiity matrix of the system Q (Σ), as in (23), shown at the bottom of the page. Therefore, the pdf f δ (m) can be cacuated as the probabiity that the system Σ, starting from a distortion eve µ, remains in the same eve for (m 1) consecutive sots, and eaves this eve at the mth sot, that is ( ) m 1 f δ (m) =π (Σ1,µ ) Q (Σ) (Σ) µ Q ( µ ) 1T where : π (Σ1,µ ) = π (Σ,µ ) Q (Σ) µ π (Σ, µ ) Q (Σ) µ 1 T. (24) The array π (Σ1,µ ) in (24) is the steady-state probabiity array in the first sot of a period in which the distortion eve is µ.the array π (Σ, µ ), on the other hand, is the steady-state probabiity array in a generic sot in which the distortion eve is other than µ, and is defined as π (Σ, µ ) = π(σ) Q (Σ) µ π (Σ) Q (Σ) µ 1 T. (25) V. C ASE STUDY A. System Characterization We anayzed the statistica characteristics of 1 hour of MPEG video sequences of the movie Evita. To encode this movie, we used a frame rate of F =25frames/s, and a frame size of 180 macrobocks. The GoP structure IBBPBB was used, seecting a ratio of tota frames to intraframes of G I =6, and the distance between two successive P frames or between the ast P frame in the GoP and the I frame in the next GoP as G P =3. The size of the transmission buffer has been set to K =60packets. The gross ink capacity assigned to the video appication is 2 Mb/s. The IP packets at the wireess termina are divided into 40 bytes bocks, as usua in the universa mobie teecommunications system (UMTS) environment. The AFEC modue encodes sets of k =16bocks into sets of m. In this case study, we use the eight-state finite-state Markov channe (FSMC) mode introduced in 26] for the wireess channe and consider two different cases. 1) Pedestrian: The mobie user s veocity is 5 km/h. 2) Driver: The mobie user s veocity is 55 km/h. Assuming that wireess transmission is performed in the 2-GHz band, which is the vaue used in UMTS, the maximum Dopper frequency is f m =10Hz in the first case and f m = 100 Hz in the second. The vaues that characterize Q are given in Tabe I for the pedestrian and driver cases. The above matrices were cacuated PSNR(n +1) µ,...,psnr(n + m 1) µ f δ (m) =Prob, PSNR(n + m) µ PSNR(n 1) µ } PSNR(n) µ (21) Q (Σ) µ ]( ) s Q,s Ñ,(i,j ), ( s Q,s Ñ,(i,j ) )] = a I (Act) Q(Σ) ( ) ( )]f Act (a i,j ), if s s Q,s Ñ,(i,j ), s Q,s Ñ,(i,j ) Q,j ) θ(a 0, otherwise (23)

2784 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 4, NO. 6, NOVEMBER 2005 TABLE I Q PARAMETERS IN THE PEDESTRIAN CASE (f m =10Hz) AND DRIVER CASE (f m = 100 Hz) TABLE II REDUNDANCY BLOCKS AND NET LINK CAPACITY OFFERED TO THE APPLICATION FOR DIFFERENT CHANNEL STATES AND TARGET ERROR PROBABILITIES ˆP IN THE DRIVER CASE,WHEN THE GROSS LINK CAPACITY IS c =2Mb/s assuming that the video-frame rate is 25 frames/s and therefore, the sot duration is =40ms. The target error-probabiity vaues considered are ˆP = 10 5, ˆP =10 4, ˆP =10 3, and ˆP =10 2. Tabe II ists, for each state i of the server SBBP mode, the vaues of m i and the resuting avaiabe ink capacities c i for these ˆP vaues in the driver case, taken as an exampe. In this case study, we wi consider a feedback aw obtained from the statistics of the movie Evita, expressed in terms of rate and distortion curves 5], 17], 23]. The rate curves R a,j (q) give the expected number of packets which wi be emitted when the jth frame in the GoP has to be encoded, if its activity vaue is a, and is encoded with a QSP vaue q. The distortion curves F (j) (q) give the expected encoding PSNR, and have been defined in Section IV. The rate and the distortion curves for the movie Evita are shown in Fig. 2. The considered feedback aw aims to maintain the number of packets in the transmission-buffer queue ower than a given threshod K θ at the end of each GoP interva, whie maintaining stabe the PSNR during the whoe GoP. In this case, both the rate curves R a,j (q) and the distortion curves F (j) (q) are used. More specificay, if we indicate the transmission-buffer queue ength and the channe avaiabe capacity when the jth frame in the GoP has to be encoded as s Q and sñ, respectivey, and a being the activity of this frame, the QSP is chosen assuming the foowing. 1) The activity wi remain constant during the rest of the GoP, that is, Act(n) =a, for each frame h j +1,G I ]. 2) The channe behavior, and therefore the avaiabe network bandwidth Ñ(n), remains constant during the rest of the GoP, that is, for each frame h j +1,G I ]. Under these assumptions, the QSP is chosen as the minimum QSP q, such that it is possibe to find a set of QSP vaues for the next frames of the GoP, q j+1,...,q GI ], so that the foowing hod. 1) The PSNR of those frames is constant, and equa to the vaue that shoud be achieved for frame j. 2) The number of emitted packets expected for the next frames of the GoP, if these QSP vaues are used, added to the current queue, minus the number of packets that wi eave the queue unti the end of the GoP, resuts to ower than the given threshod K θ.

GALLUCCIO et a.: TRANSMISSION OF ADAPTIVE MPEG VIDEO OVER TIME-VARYING WIRELESS CHANNELS 2785 Fig. 2. Rate-distortion curves for I, P, and B frames. Rate curves for (a) frame I, (b) frame B, and (c) frame P. (d) Distortion curves. In other words, the feedback aw works by choosing the QSP as in (26), shown at the bottom of the page. B. Numerica Resuts Fig. 3 shows the pdfs of the transmission-buffer queue size for the two vaues of the Dopper frequency f m and for a given vaue of the target error probabiity among those being considered. The vaues shown have been cacuated as foows: Prob S (Q) (n) =s Q }= sñ I (Ñ) sỹ I (Ỹ ) π (Σ) (s Q,sÑ,sỸ )]. (27) We can observe that the curves are basicay Gamma distributions and are very simiar to each other independenty of the ˆP vaue. This is the evidence that the feedback aw works propery. This is further demonstrated in Fig. 4 where we show the average queue size as we as the mean deay in the transmission buffer. The vaue of the average queue size does not change significanty when the ˆP changes and is higher in the driver case. This can be expained by the fact that in the driver case, the wireess medium quaity is ower and therefore, the transmission-buffer service rate is ower. Simiar discussions can be carried out concerning Fig. 5, where the performance in terms of oss probabiity in the transmission buffer is shown and cacuated as in 4]. q = φ(s Q,a,j) = min q 1,31] q such that q j+1,...,q GI ] for which : F (k) (q k )=F (j) ( q) k j +1,...,G I ] s Q + R a,j ( q)+ G I k=j R a,j(q k ) (G I j +1) Ñ(n) K θ (26)

2786 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 4, NO. 6, NOVEMBER 2005 Fig. 3. Transmission-buffer size pdf for ˆP =10 2 (a) in the pedestrian case and (b) in the driver case. Fig. 4. Average transmission-buffer size and mean deay versus the target error probabiity ˆP. Fig. 6 shows the performance reated to the encoding quaity. In particuar, it can be observed that, for high vaues of ˆP, due to the high amount of avaiabe bandwidth, the most ikey PSNR eve is the highest. On the contrary, for ow vaues of ˆP, as a resut of the arge amount of redundancy introduced by AFEC, the avaiabe bandwidth is ow, and therefore, the video source reduces the encoding quaity. For this reason, the ower the vaue of the target in the wireess ink ˆP, the greater the probabiity of poorer PSNR eves. In order to better quantify the infuence of the choice of the target vaue ˆP on the encoding performance, in Fig. 6, the average PSNR eve is shown. As expected, the worst case for the average PSNR eve is given when the AFEC has a very stringent target for the maximum ˆP. When a ess stringent target vaue for the is required, the encoding quaity increases. Obviousy, the average PSNR vaue, and thus encoding quaity, is higher in the pedestrian case. VI. CONCLUSION In this paper, we have defined an anaytica framework for the evauation of the performance of rea-time MPEG video transmission over a wireess ink that appies AFEC to keep the beow a given threshod. The MPEG encoder uses a rate controer that adapts the output rate by appropriatey setting the QSP to foow the bandwidth variations whie maximizing encoding quaity and stabiity. The whoe system has been modeed by an emission process that feeds the transmission buffer; the server of this buffer behaves according to the channe conditions, i.e., the

GALLUCCIO et a.: TRANSMISSION OF ADAPTIVE MPEG VIDEO OVER TIME-VARYING WIRELESS CHANNELS 2787 Fig. 5. Packet oss probabiity in the transmission buffer versus the target error probabiity ˆP. Fig. 6. Average PSNR eve versus the target error probabiity ˆP. service rate is higher when channe conditions are good and ower when channe conditions are bad. SBBPs have been used to mode both the MPEG video source 4], 15], 17] and the server process of the transmission buffer that coincides with the time-varying avaiabe bandwidth in the network. Accordingy, the whoe system has been modeed as an SBBP/SBBP/1/K process. The anaytica framework proposed in the paper has been used to evauate the performance in terms of the distortion introduced by the quantization mechanism in the encoding process, which are the oss and mean deay in the transmission buffer. Numerica resuts show that our system is very robust and reiabe due to the impemented feedback aw that maintains amost constant the mean deay and the oss probabiity in the output buffer. Moreover, the corruption probabiity in the wireess channe is aso imited in spite of possibe variations in time in the wireess-channe BER. The proposed mode aows the designer to evauate the introduced encoding quaity variation that represents the cost of using this approach. The resuts obtained in the paper can be used to obtain the best tradeoff between encoding quaity and information correctness.

2788 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 4, NO. 6, NOVEMBER 2005 REFERENCES 1] I. F. Akyidiz, I. Joe, H. Driver, and Y. L. Ho, A new adaptive FEC scheme for wireess ATM networks, in Proc. IEEE Miitary Communications Conf. (MILCOM), Boston, MA, Oct. 1998, pp. 277 281. 2] E. Atman, C. Barakat, and V. M. Ramos, Queueing anaysis of simpe FEC schemes for IP teephony, in Proc. IEEE Information Communications (INFOCOM), Anchorage, AK, Apr. 2001, pp. 796 804. 3] J. J. Bae, T. Suda, and R. Simha, Anaysis of individua packet oss in a finite buffer queue with heterogeneous Markov moduated arriva processes: A study of traffic burstiness and a priority packet discarding, in Proc. IEEE Information Communications (INFOCOM), Forence, Itay, Apr. 1992, pp. 219 230. 4] A. Cernuto, F. Cocimano, A. Lombardo, and G. Schembra, A queueing system mode for the design of feedback aws in rate-controed MPEG video encoders, IEEE Trans. Circuits Syst. Video Techno.,vo.12,no.4, pp. 238 255, Apr. 2002. 5] C. F. Chang and J. S. Wang, A stabe buffer contro strategy for MPEG coding, IEEE Trans. Circuits Syst. Video Techno., vo. 7, no. 6, pp. 920 924, Dec. 1997. 6] S. R. Cho, Adaptive error contro scheme for mutimedia appications in integrated terrestria-sateite wireess networks, in Proc. IEEE Wireess Communications and Networking Conf. (WCNC), Chicago, IL, Sep. 2000, pp. 629 633. 7] A. Chockaingam and M. Zorzi, Wireess TCP performance with ink ayer FEC/ARQ, in Proc. IEEE Int. Conf. Communications (ICC), Vancouver, BC, Canada, Jun. 1999, pp. 1212 1216. 8] W. Ding and B. Liu, Rate contro of MPEG video coding and recording by rate-quantization modeing, IEEE Trans. Circuits Syst. Video Techno., vo. 6, no. 1, pp. 12 20, Feb. 1996. 9] O. Hashida et a., Switched batch Bernoui process (SBBP) and the discrete-time SBBP/G/1 queue with appication to statistica mutipexer, IEEE J. Se. Areas Commun., vo. 9, no. 3, pp. 394 401, Apr. 1991. 10] A. E. Kama, Efficient soution of mutipe server queues with appication to the modeing of ATM concentrators, in Proc. IEEE Information Communications (INFOCOM), San Francisco, CA, 1996, pp. 248 254. 11] A. La Corte, A. Lombardo, and G. Schembra, An anaytica paradigm to cacuate mutipexer performance in an ATM mutimedia environment, Comput. Netw. ISDN Syst., vo. 29, no. 16, pp. 1881 1900, Dec. 1997. 12] L. J. Lin and A. Ortega, Bit-rate contro using piecewise approximated rate-distortion characteristics, IEEE Trans. Circuits Syst. Video Techno., vo. 8, no. 4, pp. 446 459, Aug. 1998. 13] D. V. Lindey, The theory of queues with a singe server, Proc. Cambridge Phios. Soc., vo. 48, pp. 277 289, 1952. 14] H. Liu and M. E Zarki, Performance of H.263 video transmission over wireess channes using hybrid ARQ, IEEE J. Se. Areas Commun., vo. 15, no. 9, pp. 1775 1786, Dec. 1997. 15] A. Lombardo, G. Morabito, and G. Schembra, An accurate and treatabe Markov mode of MPEG-video traffic, in Proc. IEEE Information Communications (INFOCOM), San Francisco, CA, Mar./Apr. 1998, pp. 217 224. 16] A. Lombardo, G. Morabito, S. Paazzo, and G. Schembra, A Markovbased agorithm for the generation of MPEG sequences matching intraand inter-gop correation, Eur. Trans. Teecommun. J., vo. 12, no. 2, pp. 127 142, Mar./Apr. 2001. 17] A. Lombardo and G. Schembra, Performance evauation of an adaptiverate MPEG encoder matching intserv traffic constraints, IEEE/ACM Trans. Netw., vo. 11, no. 1, pp. 47 65, Feb. 2003. 18] M. F. Neutz, Matrix-Geometric Soutions in Stochastic Modes: An Agorithmic Approach. Batimore, MD: The Johns Hopkins Univ. Press, 1981. 19] L. Rabiner, A tutoria on hidden Markov modes and seected appications in speech recognition, Proc. IEEE, vo. 77, no. 2, pp. 257 286, Feb. 1989. 20] A. Ramesh, A. Chockaingam, and L. B. Mistein, A first-order Markov mode for correated Nagakami-m fading channes, in Proc. IEEE Int. Conf. Communications (ICC), New York, Apr. 2002, pp. 3413 3417. 21] O. Rose, Statistica properties of MPEG video traffic and their impact on traffic modeing in ATM systems, Univ. Würzburg, Inst. Comput. Sci., Würzburg, Germany, Tech. Rep. 101, Feb. 1995. 22] G. M. Schuster and A. K. Katsaggeos, Rate-Distortion Based Video Compression, Optima Video Frame Compression and Object Boundary Encoding. Norwe, MA: Kuwer, 1997. 23] T. Takine, T. Suda, and T. Hasegawa, Ce oss and output process anayses of a finite-buffer discrete-time ATM queueing system with correated arrivas, in Proc. IEEE Information Communications (INFOCOM), San Francisco, CA, Mar. 1993, pp. 1259 1269. 24] C. C. Tan and N. C. Beauieu, On first-order Markov modeing for the Rayeigh fading channes, IEEE Trans. Commun., vo. 48, no. 12, pp. 2032 2040, Dec. 2000. 25] B. Vucetic, An adaptive coding scheme for time-varying channes, IEEE Trans. Commun., vo. 39, no. 5, pp. 653 663, May 1991. 26] H. S. Wang and N. Moayeri, Finite-state Markov channe A usefu mode for radio communication channes, IEEE Trans. Veh. Techno., vo. 44, no. 1, pp. 163 171, Feb. 1995. 27] M. Zorzi and R. R. Rao, On the statistics of bock errors in bursty channes, IEEE Trans. Commun., vo. 45, no. 6, pp. 660 667, Jun. 1997. 28] M. Zorzi, R. R. Rao, and L. B. Mistein, Error statistics in data transmission over fading channes, IEEE Trans. Commun., vo. 46, no. 11, pp. 1468 1477, Nov. 1998. 29] Coded Representation of Picture and Audio Information, MPEGTest Mode 5. ISO-IEC/JTC1/SC29/WG11, Apr. 1993. 30] Coded Representation of Picture and Audio Information, MPEGTest Mode 2. Internationa Standard ISO-IEC/JTC1/Sc29/WG11, Ju. 1992. 31] Coding of Moving Pictures and Associated Audio for Digita Storage Media up to 1.5 Mb/s Part 2, Video, Internationa Standard ISO- IEC/JTC1/SC29/WG11, DIS11172-1, Mar. 1992. Laura Gauccio received the Laurea degree in eectrica engineering and the Ph.D. degree in eectrica, computer and teecommunications engineering, both from the University of Catania, Catania, Itay, in 2001 and 2005, respectivey. Since 2002, she has been with the Itaian Nationa Consortium of Teecommunications (CNIT), where she is working as a Research Feow within the Virtua Immersive Communications (VICOM) Project. From May to Juy 2005, she was a Visiting Schoar at the COMET Group, Coumbia University, New York, NY. Her research interests incude ad hoc and sensor networks, protocos and agorithms for wireess networks, and network performance anaysis. Dr. Gauccio served and wi serve in the Program Committee of the 4th Academic Network for Wireess Internet Research in Europe (ANWIRE) Internationa Workshop on Wireess Internet and Reconfigurabiity, the 20th Internationa Symposium on Computer and Information Sciences (ISCIS 05), and Networking 2006. Giacomo Morabito (M 02) received the Laurea degree in eectrica engineering and the Ph.D. degree in eectrica, computer, and teecommunications engineering from the University of Catania, Catania, Itay, in 1996 and 2000, respectivey. From November 1999 to Apri 2001, he was with the Broadband and Wireess Networking Laboratory of the Georgia Institute of Technoogy as a Research Engineer. Since May 2001, he has been with the Schoo of Engineering at Enna of the University of Catania, where he is currenty an Assistant Professor. He is serving as a Guest Editor on the editoria board of Computer Networks and Mobie Networks and Appications (MONET). He is aso a Member of the technica program committee of severa conferences. Moreover, he has been the Technica Program Co-Chair of Med-Hoc-Net 2004. His research interests incude mobie and sateite networks, sef-organizing networks, quaity of service (QoS), and traffic management. Dr. Morabito is serving on the Editoria Board of IEEE Wireess Communications Magazine. Giovanni Schembra received the degree in eectrica engineering from the University of Catania, Catania, Itay, in 1991. Working in the teecommunications area, he received the Master s degree from CEFRIEL, Mian, Itay, in 1992, with his thesis focusing on the anaytica performance evauation in an ATM network. He received the Ph.D. degree in eectronics, computer science, and teecommunications engineering with a dissertation on mutimedia traffic modeing in a broadband network. He is currenty an Assistant Professor in Teecommunications at the University of Catania.