Problems of high DFE coefficients

Problems of high DFE coefficients Yasuo Hidaka Fujitsu Laboratories of America, Inc. September, 5 IEEE P8.3by 5 Gb/s Ethernet Task Force

Abstract If we allow high DFE coefficients, we cannot meet MTTFPA (Mean Time to False Packet Acceptance) requirements at BER=E- due to burst errors Hence, (max magnitude of relative DFE coefficient) is proposed to be.35 There are some serious problems with =.35 or.5 Problem : COM is not accurate when < Problem : BER (and COM) may be drastically degraded when is.35 or.5 COM should not be used with <, because COM is not accurate when < (Problem ) This may be fixed in the future =.35 rejects sufficiently good channels (Problem ) =.35 is not necessary to meet the MTTFPA requirement We have two other options to satisfy the MTTFPA requirement: Option : Revise COM criteria so that we get BER<E-5, if we pass COM test with DER=E-, and Test Rx for BER<E- with restricted DFE coefficients, or for BER<E-5 with no restriction Option : Use precoding to eliminate burst errors due to DFE error propagation IEEE P8.3by 5 Gb/s Ethernet Task Force

Study of Effect on COM and BER (n).,.5,.35 (for all n) CTLE : fb/4, fb/5, fb/6 fz: same as DC gain: min -db, max db, step db when = fb/4 or fb/5 min -8dB, max db, step.5db when = fb/6 Channel data 3m cable: B(3Q4) fair, G(6QQ) typical, H(6Q4) good 5m cable: Q(4QQ) fair, N(6QQ) typical, R(4QQ) good Test conditions Test (PKG trace = mm) and Test (PKG trace = 3mm) DER = E- Equalizer parameters: optimized by reference COM code (i.e. http://www.ieee8.org/3/bj/public/tools/ran_com_3bj_3bm 4.zip) BER and Eye: analyzed by in-house tool Parameters of statistical analysis: TX RJ =.UI (rms), TX DJ =.5UI ( - ), TX EOJ =.35UI (p-p) RX RJ =.5UI (rms), RX DJ =.75UI ( - ), RX EOJ =.75UI (p-p) TX output noise SNR TX = 7 (db) RX input noise = 5.E-8 (V /GHz) Receiver 3dB bandwidth =.75 (fb) IEEE P8.3by 5 Gb/s Ethernet Task Force

Effect of on COM and BER for 3m Cable vs COM (DER=E-) 5 4 3 3m Cable (=.) fb/4 fb/5 fb/6 5 4 3 3m Cable (=.5) fb/4 fb/5 fb/6 Case A 4 3 3m Cable (=.35) Case B fb/4 fb/5 fb/6 vs BER log(ber) 5 3 3m Cable (=.) fb/4 fb/5 fb/6 log(ber) 5 3 3m Cable (=.5) fb/4 fb/5 fb/6 5 5 3 fb/4 fb/5 fb/6 Case A Case B COM and BER are roughly consistent when =. COM and BER are very inconsistent when =.5 or.35 log(ber) 3m Cable (=.35) 3 IEEE P8.3by 5 Gb/s Ethernet Task Force

Effect of on COM and BER for 5m Cable vs COM (DER=E-) 5m Cable (=.) 5m Cable (=.5) 5m Cable (=.35) 3 3 3 4 fb/4 fb/5 fb/6 fb/4 fb/5 fb/6 fb/4 fb/5 fb/6 vs BER 5m Cable (=.) 5m Cable (=.5) 5m Cable (=.35) 5 5 log(ber) log(ber) log(ber) 5 5 fb/4 fb/5 fb/6 fb/4 fb/5 fb/6 fb/4 fb/5 fb/6 COM and BER are roughly consistent when =. COM and BER are very inconsistent when =.5 or.35 4 IEEE P8.3by 5 Gb/s Ethernet Task Force

Effect of on COM vs COM (3m Cable) 3m Cable (=fb/4) 3m Cable (=fb/5) 3m Cable (=fb/6) 4 3 5 4 3 6 4..5.35..5.35..5.35 vs COM (5m Cable) 5m Cable (=fb/4) 5m Cable (=fb/5) 5m Cable (=fb/6) 3 4 4 4 4..5.35..5.35..5.35 COM is not much affected by when = fb/4 COM is largely degraded by when = fb/5 or fb/6 5 IEEE P8.3by 5 Gb/s Ethernet Task Force

Effect of on BER vs BER (3m Cable).E-9 3.E-4 8.8E-9.E- 3m Cable (=fb/4) 5.E- 3m Cable (=fb/5) 3m Cable (=fb/6) log(ber) 5 log(ber) 5 3 log(ber) 5 5 3..5.35..5.35..5.35 vs BER (5m Cable) 5m Cable (=fb/4) 5m Cable (=fb/5) 5m Cable (=fb/6) 5 log(ber) 5 log(ber) log(ber) 5..5.35..5.35..5.35 BER is not affected by when = fb/4 BER is largely degraded by when = fb/5 or fb/6 3m T(B) is good with =fb/6 and =, but fails with =.35 6 IEEE P8.3by 5 Gb/s Ethernet Task Force

Detail Analysis of Case A and Case B Channel: 3m cable H(6Q4), Test, =.35 Case A (=fb/4) DCgain = - db, b() =.337389 (not restricted) COM (DER=E-) 3.5463 db (reference implementation) 3.7644 db (our implementation) BER = 3.6E-3 Case B (=fb/6) DCgain = -6.5 db, b() =.35 (restricted by ) COM (DER=E-).56 db (reference implementation).37456 db (our implementation) BER =.6E- Little data dependence at the best phase. This is OK. Large data dependence at the best phase. This causes the problem. -- -- -- -- 7 IEEE P8.3by 5 Gb/s Ethernet Task Force

Two Options to meet the MTTFPA requirements Option Revise COM criteria (currently 3dB) so that there is enough margin To achieve BER<E-5, when we pass the COM test with DER=E- Statistically guarantee the channel quality so that we can achieve BER<E-5 I am currently working on this statistical calculation Test Rx for BER<E-5 with no restrictions on DFE coefficients For a combination of compliant channel and Rx, since BER will be less than E-5, we will meet the MTTFPA requirement We may use other means such as plotting a bathtub curve to shorten test time I have considered an alternative Rx test for BER<E- with DFE coefficients <.35, but such an alternative test is not acceptable For some good channels, BER can be <E-5 with high DFE coefficients, whereas BER is degraded >E-, if high DFE coefficients are not allowed Such good channels have high loss in high frequency due to material loss, but the channel design is good enough, because we can achieve sufficiently low BER. I think such good design channels should be accepted as compliant. Option Use precoding to eliminate burst errors due to DFE error propagation This is a simple solid solution (next page) 8 IEEE P8.3by 5 Gb/s Ethernet Task Force

Precoding Tx side: encode the transmitting data by b(k) = b(k-)^a(k) Rx side: decode the received data by a (k) = b(k)^b(k-) ^: an exclusive-or operator a(k): original data sequence b(k): transferred data sequence (NRZ) a (k): recovered data sequence Any burst error on b(k) from k to k (k<=k) is converted to two errors on a (k), one at a (k), and another at a (k+) Hence, it eliminates any burst errors This is essentially in the same principle as precoding in Duobinary signaling, or precoding in KP4 (although it is a variant for PAM4). We cannot omit DFE to achieve low BER. That is a difference from Duobinary signaling. Minor drawbacks If there is no error propagation, BER for random error is doubled I think this is OK, because the packet is anyway dropped, or protected by FEC If there is no DFE, unnecessary extra circuit is required I think this is OK, because DFE is commonly used The encoder has a critical path of an exclusive OR within UI I think this is achievable I don t know why this hasn t been discussed (maybe everyone is too busy), but I believe this is a solid solution and better than restricting high DFE coefficients Is it too late to discuss this scheme? Or, am I missing something? 9 IEEE P8.3by 5 Gb/s Ethernet Task Force

Appendix IEEE P8.3by 5 Gb/s Ethernet Task Force

Difference between COM and our BER analysis COM Directly calculate a single probability distribution (i.e. PDF or CDF) Jitter is added at all ISI locations Our BER analysis Calculate multiple (4 for NRZ, 3 for PAM4) probability distributions for all the combinations of prior, next, and cursor symbol levels # of cursor symbol levels is half, because of vertical symmetry Jitter is added differently for each distribution, taking account of each transition Jitter at is smaller than at or, because derivative is cancelled and small No jitter is added for distribution at sequence, because there is no transition Final CDF is the worst case that is the max value of multiple CDFs: max max Here, and are CDFs and are PDFs. Coefficient is for the fact that this is only for lower side of the entire final CDF: max, max, min No jitter is added at ISI locations other than between prior symbol and cursor symbol or between cursor symbol and next symbol Due to this difference, estimated BER is a little lower than DER when COM is db IEEE P8.3by 5 Gb/s Ethernet Task Force

Very Detail Analysis of Case A and Case B Case A (=fb/4) COM analysis (our implementation) Case B (=fb/6) COM analysis (our implementation) Notation: PDF(μ,σ), μ=mean, σ=rms PDF: As=μ=8.mV, σ=.mv, Ani=.8mV~5.9σ COM=*log(8.mV/.8mV)=3.7dB BER=P(-As)=5.3E-3 BER analysis (vertical PDF/CDF at the best phase) PDF: As=μ=7.8mV, σ=5.mv, Ani=3.7mV~4.6σ COM=*log(7.8mV/3.7mV)=.38dB BER=P(-As)=.5E-9 σ and BER are much larger (COM is smaller) than Case A BER analysis (vertical PDF/CDF at the best phase) *PDF worst (μ=6.7,σ=.4) follows PDF (μ=6.8,σ=.6) *PDF worst (μ=.,σ=.9) follows PDF (μ=.,σ=.9) σ of PDF & PDF is smaller than PDF & PDF μ is similar between PDFs with respect to σ value σ of PDF & PDF is smaller than PDF & PDF μ of PDF and PDF are quite different w.r.t. σ value σ of *PDF worst and BER are similar to Case A IEEE P8.3by 5 Gb/s Ethernet Task Force

Suggestions for COM In our BER analysis, use of multiple distributions was the key to obtain satisfactory results for test cases where a single large ISI (i.e. the largest ISI) is close to the RSS value of all ISIs Our BER analysis is not necessarily the best, but probably better than COM COM is very likely inaccurate when a DFE coefficient is restricted by <, because restriction of a DFE coefficient causes the single large residual ISI close to the RSS value We may fix the COM formula in a similar way to our BER analysis, but I have not come to a complete suggestion yet I may provide it later, but it takes some time In the mean time, it is OK to use the current COM with = and high tap-count DFE, because no single large ISI is left after DFE cancels major ISIs In fact, I do not see a large discrepancy between COM and BER as long as I use = 3 IEEE P8.3by 5 Gb/s Ethernet Task Force

References [] http://grouper.ieee.org/groups/8/3/by/public/may5/ sun_3by 55.pdf [] http://www.ieee8.org/3/by/public/adhoc/architecture/ sun_65_5ge_adhoc.pdf 4 IEEE P8.3by 5 Gb/s Ethernet Task Force

References of Channel Data ~ = http://www.ieee8.3.org/3/ 3 meter cable assembly A: ~/GCU/public/ChannelData/CD 45/3m_QSFP_3AWG.zip (Tx-Rx.s4p) B: ~/by/public/channel/te_qsfp_4sfp_3m_3awg.zip (TE_3m3AWG_QSFP_4SFP_P_TX_P_RX_THRU.s4p) C: ~/GCU/public/ChannelData/Molex 56/bugg 5.zip (3m 3AWG Unicore/Cable /P RX/TX.s4p) D: ~/by/public/channel/te_qsfp_4sfp_3m_8awg.zip (TE_3m8AWG_QSFP_4SFP_P_TX_P_RX_THRU.s4p) E: ~/by/public/channel/te_qsfp_qsfp_3m_6awg_maxlossexample_5p993db.zip F: ~/by/public/channel/amphenol_ndacgj-3-qsfp-4sfp_3m_6awg_apn43433hxj.zip (PTX_PRX.s4p) G: ~/GCU/public/ChannelData/Molex 56/bugg 5.zip (3m 6AWG leoni/p RX/TX.s4p) H: ~/by/public/channel/te_qsfp_4sfp_3m_6awg.zip (TE_3m6AWG_QSFP_4SFP_P_TX_P_RX_THRU.s4p) J: ~/by/public/channel/te_qsfp_qsfp_3m_5awg_maxlossexample_5p35db.zip K: ~/by/public/channel/te_qsfp_qsfp_3m_4awg_maxlossexample_4p49db.zip L: ~/by/public/channel/te_qsfp_4sfp_3m_4awg.zip (TE_3m4AWG_QSFP_4SFP_P_TX_P_RX_THRU.s4p) 5 meter cable assembly M: ~/GCU/public/ChannelData/CD 45/5m_QSFP_6AWG.zip (Tx-Rx.s4p) N: ~/GCU/public/ChannelData/Molex 56/bugg 5.zip (5m 6AWG Leoni/P RX/TX.s4p) P: ~/by/public/channel/amphenol_ndacgj-5-qsfp_4sfp_5m_6awg_apn44453hyt.zip(ptx_prx.s4p) Q: ~/GCU/public/ChannelData/Molex /5m/5m_all.zip (P RX/TX.s4p) R: ~/GCU/public/ChannelData/molex 3/cableb_bugg_3_3.zip (PRX/PTX.s4p) 5 IEEE P8.3by 5 Gb/s Ethernet Task Force

Thank you 6 IEEE P8.3by 5 Gb/s Ethernet Task Force