Submission Title: [Rate 1/4 code for TG4a] Sep 2005 Project: IEEE P802.15 Working Group for Wireless Personal Area Networks (WPANs) Submission Title: [Rate 1/4 code for TG4a] Date Submitted: [22-Sep-2005] Source: [Michael Mc Laughlin] Company [Decawave Ltd.] Address [25 Meadowfield, Sandyford, Dublin 18, Ireland] Voice:[+353−1−2954937 ], FAX: [What’s a FAX?], E−Mail: [michael@decawave.com] Re: [802.15.4a.] Abstract: [Proposes a FEC scheme for TG4a data] Purpose: [To promote discussion in 802.15.4a.] Notice: This document has been prepared to assist the IEEE P802.15. It is offered as a basis for discussion and is not binding on the contributing individual(s) or organization(s). The material in this document is subject to change in form and content after further study. The contributor(s) reserve(s) the right to add, amend or withdraw material contained herein. Release: The contributor acknowledges and accepts that this contribution becomes the property of IEEE and may be made publicly available by P802.15. Mc Laughlin, Decawave

FEC Options 1 – 5 FEC 1 FEC 2 FEC 3 FEC 4 FEC 5 Sep 2005 SOC K= 3,4 or 5 R = ½ or ¼ Coherent Receiver: True Rate = ¼ Non Coherent Receiver: Equivalent to Rate = 1 or ½ (Rate ½ or ¼ before erasures) FEC 1 Convolutional Encoder K= 3,4 or 5 R= 1/4 Coherent Receiver: True Rate = ¼ Non Coherent Receiver: Equivalent to Rate = ½ (Rate ¼ before erasures) FEC 2 Systematic Convolutional Encoder K= 3,4 or 5 R = 1/2 Convolutional Encoder K=3, R= 1/2 FEC 3 Coherent Receiver: Concatenated code, Rate = ¼ Non Coherent Receiver: Convolutional code, Rate = ½ Systematic Convolutional Encoder K= 3,4 or 5 R = 1/2 BCH or RS GF(28): RS(40,32) GF(26): RS(43,53) Coherent Receiver: Concatenated code Rate = 0.4 Non Coherent Receiver: RS code, Rate = 0.8 FEC 4 Systematic Convolutional Encoder K= 3,4 or 5 R= 1/2 Coherent Receiver: Convolutional code Rate = ½ Non Coherent Receiver: Uncoded FEC 5 Mc Laughlin, Decawave

Example FEC Option 3 XOR XOR Sign Pos’n data in XOR Sign Pos’n XOR Sep 2005 Example FEC Option 3 XOR XOR Sign data in Pos’n XOR Sign XOR Pos’n Inner code: K=3 g1=05, g2=02 (systematic) Outer code: Rate ½ K=3 g1=07, g2=05 Mc Laughlin, Decawave

Same as FEC Option 2 Sign XOR data in Pos’n XOR XOR Sign XOR Pos’n Sep 2005 Same as FEC Option 2 XOR Sign data in XOR Pos’n XOR Sign XOR Pos’n Overall code: Rate ¼ K=5 g1=35, g2=16, g3=21, g4=12 Mc Laughlin, Decawave

Option 3 is subset of Option 2 Sep 2005 Option 3 is subset of Option 2 Option 2: Each coded bit is a generated by a combination of 2 polynomials All Option 3 polynomial combinations can be generated by Option 2 Converse is not true Best FEC 2 at least as good as Best FEC 3 Mc Laughlin, Decawave

Rate ¼ Coherent - Coherent receiver sees all 4 generators e.g. Sep 2005 Rate ¼ Coherent - Coherent receiver sees all 4 generators e.g. g1=25, g2=12, g3=23, g4=16 k=5 dfree=15 # parallel paths=1 Mc Laughlin, Decawave

Sep 2005 Non Coherent Receiver See rate ¼ convolutional code punctured to rate ½ g2=12, g4=16 => Rate ½ K=4 dfree = 5 about 3.0dBs performance improvement over uncoded at 10-2 8 state decoder Mc Laughlin, Decawave

Rate ¼ K=5 Performance Sep 2005 Mc Laughlin, Decawave AWGN PER for Rate 1/4 K=5 g=[25,12,23,16] (Blue) and Rate 1/2 K=5 10 10 -1 PER 10 -2 g = 33,02 non-antipodal (Option 3 coherent) g = 33,02 non-antipodal (Option 3 non-coherent) g = 35,23 antipodal (Option I) 10 -3 Coherent rate 1/4 K=5 Non-coherent rate 1/4 K=5 (Eff K=4) 10 -4 2 4 6 8 10 12 14 Eb/No Mc Laughlin, Decawave

Lower Complexity K=4, Rate ¼ Code Sep 2005 Lower Complexity K=4, Rate ¼ Code g1=17, g2=04, g3=15, g4=06 Coherent Receiver sees all generators k=4, dfree=13, # parallel paths=2 Exactly the same as best BPSK K=4 Rate ¼ code Non-Coherent Receiver sees only g2 and g4 g2=04, g4=06 k=3, dfree=3, # parallel paths=1 Compare to best dfree of 5 for k=3 Mc Laughlin, Decawave

Sub Optimal K=4, Rate ¼ code Sep 2005 Sub Optimal K=4, Rate ¼ code g1=17, g2=04, g3=15, g4=07 Coherent Receiver sees all generators dfree=12, k=4 # parallel paths=1 lose ~0.35dB for dfree, gain ~0.2dB for #parallel paths overall lose ~0.15dB Non-Coherent Receiver sees g2 and g4 g2=04, g4=07 k=3, dfree=4, # parallel paths=1 Compare to best dfree of 5 for k=3 Mc Laughlin, Decawave

Compare K=4, Rate ¼ and K=5, Rate ½ Sep 2005 Compare K=4, Rate ¼ and K=5, Rate ½ AWGN PER for K=4, Rate 1/4 and K=5 Rate 1/2 2 4 6 8 10 12 14 -4 -3 -2 -1 PER [17,04,15,06] Coherent [17,04,15,06] Non-coherent [17,04,15,07] Non Coherent [17,04,15,07] Coherent g = 33,02 non-antipodal (Option 10 coherent) g = 33,02 non-antipodal (Option 10 non-coherent) g = 35,23 antipodal (Option I) Eb/No Mc Laughlin, Decawave

Rate ¼ K=4 and K=5 Performance Sep 2005 Rate ¼ K=4 and K=5 Performance AWGN PER for Rate 1/4 K=4, Rate 1/4 K=5 and and Rate 1/2 K=5 10 10 -1 -2 PER 10 K=4 Rate ¼ Optimal Coherent K=4 Rate ¼ Opimal Non-Coh K=5 Rate ¼ Non Coherent K=5 Rate ¼ Coherent 10 -3 g = 33,02 non-antipodal (Option 10 coherent) g = 33,02 non-antipodal (Option 10 non-coherent) g = 35,23 antipodal (Option I) 10 -4 2 4 6 8 10 12 14 Eb/No Mc Laughlin, Decawave

K=4 Optimal vs Sub Optimal Sep 2005 K=4 Optimal vs Sub Optimal 2 4 6 8 10 12 14 -4 -3 -2 -1 AWGN PER for Rate 1/4 K=4 g=[17,04,15,06] and g=[17,04,15,07] Eb/No PER [17,04,15,06] Coherent [17,04,15,06] Non-coherent [17,04,15,07] Coherent [17,04,15,07] Non-coherent Mc Laughlin, Decawave

Rate ¼ need 4 bits / uncoded bit Sep 2005 Rate ¼ need 4 bits / uncoded bit ~1000ns 2 codes transmitted every microsecond Mc Laughlin, Decawave

Original Option 1 Proposal Sep 2005 Original Option 1 Proposal ~1000ns 2 codes transmitted every microsecond Mc Laughlin, Decawave

Summary The K=4, rate ¼, sub-optimal code is recommended (17,04,15,07) Sep 2005 Summary The K=4, rate ¼, sub-optimal code is recommended (17,04,15,07) Coherent performance as good or better than Rate ½ K=5 Non-Coherent performance also very good. 1% PER at ~10.5dB Eb/No 8 state, each state 2 possible outputs =>low complexity decoder Systematic code => allows receiver without viterbi Mc Laughlin, Decawave