1. Tang et al. Slide 1 Achieving Full Rate Network Coding with Constellation Compatible Modulation & Coding Suhua Tang Hiroyuki YOMO, Tetsuro UEDA, Ryu MIURA, Sadao OBANA ATR Adaptive Communications Research Laboratories, Japan Dec. 7, 2010 GlobeCom 2010, Miami, Florida, USA

2. Tang et al. Slide 2 Outline Relay with network coding (NC) –Rate-mismatch problem Re-interpretation of network coding Proposed scheme –FRNC: full-rate network coding Simulation evaluation Conclusion

3. Tang et al. Slide 3 Relay with Network Coding Relay with network coding 2 packets exchanged within 3 slots M1M1 RM2M2 T1:XT1:X T3:X㊉YT3:X㊉Y T2:YT2:Y Network coding improves relay efficiency: Larsson’06 [3], Popovski’06 [4] –Exploiting broadcast nature and a priori information Plain decode-and-forward 2 packets exchanged within 4 slots M1M1 RM2M2 T1:XT1:X T3:XT3:X T4:YT4:Y T2:YT2:Y Decode and forward improves system reliability M1M1 M2M2 T1:XT1:X T2:YT2:Y Direct transmission  High outage prob. (w/o RA) or low rate (w/ RA) Wireless access network (Wireless LAN, cellular network) Internet M1M1 M 2 (AP) content server (X ㊉ Y) ㊉ X → Y (X ㊉ Y) ㊉ Y → X Direct transmission 2 packets exchanged within 2 slots RA: rate adaptation

4. Tang et al. Slide 4 What Limits NC’s Performance? Factors affecting performance of network coding Rate mismatch –R  M 1 /M 2, NC (min rate): min(r 1,r 2 ) –NC is not beneficial if min(r 1,r 2 ) is much less than max(r 1, r 2 ) –min(r 1,r 2, …, r n ) gets smaller as n increases When does rate mismatch occur? –R is not in the middle  Different average gains –R is in the middle  Different instantaneous gains (fading) 1000byte 500byte M1M1 RM2M2 T 3 :X ㊉ Y, 6Mbps r 1 =6Mbps r 2 =54Mbps Rate mismatchPacket length mismatchLack of a priori information M1M1 R M3M3 T3:X㊉YT3:X㊉Y M2M2 T1:XT1:X T2:YT2:Y X Y M1M1 RM2M2 T3:X㊉YT3:X㊉Y M1M1 RM2M2 M1M1 RM2M2 M1M1 RM2M2 r 1 =6Mbps r 2 =54Mbps r 1 =36Mbps r 2 =24Mbps Y

5. Tang et al. Slide 5 Efforts to Solve Rate Mismatch Previous works –Two-way-relay Larsson’08 [9] Constant envelope modulation (PSK) Koike-Akino’08 [10] QPSK, 5-ary PSK Alimi’08 (iPack) [12] Superposition coding + network coding –Multiple-way-relay Yomo’09(NCSched) [8] Opportunistic scheduling Our aim: a complete solution –Dirty paper coding [Costa’83] tells us this is possible –Policy: constellation compatible modulation & coding (nesting constellation & retain min-distance) min-rate Full rate : broadcast the network coded packet, using the highest rate on each link M1M1 RM2M2 T 3 :X ㊉ Y, 6Mbps r 1 =6Mbps r 2 =54Mbps YX M1M1 RM2M2 T3:X㊉YT3:X㊉Y 6Mbps54Mbps YX r 1 =6Mbps r 2 =54Mbps

6. Tang et al. Slide 6 Re-interpretation of Network Coding Relay transmits network coded message With a priori info, each node has different interpretation Rate is mainly limited by constellation size Same constellation size  rate mismatch Remove rate mismatch by using different levels of constellation together, e.g., QPSK+16QAM? S 0 : 00 S 1 : 01S 3 : 11 S 2 : 10 0x1x x1 x0 S B1 : 01 S B0 : 00S B2 : 10 S B3 : 11 0x1x x0 x1 R transmits XORed sum a 1 a 0 ㊉ b 1 b 0 =10 At receiver M 2 Constellation for b 1 b 0 (a 1 a 0 =01 known a priori) 01 ㊉ 00 = 01 => S B0 01 ㊉ 01 = 00 => S B1 01 ㊉ 10 = 11 => S B2 01 ㊉ 11 = 10 => S B3 S A3 : 11 S A2 : 10S A0 : 00 S A1 : 01 1x0x x0 x1 At receiver M 1 Constellation for a 1 a 0 (b 1 b 0 =11 known a priori) 00 ㊉ 11 = 11 => S A0 01 ㊉ 11 = 10 => S A1 10 ㊉ 11 = 01 => S A2 11 ㊉ 11 = 00 => S A3 M1M1 RM2M2 T1:b1b0T1:b1b0 T 3 :b 1 b 0 ㊉ a 1 a 0, QPSK T2:a1a0T2:a1a0 r 1 (QPSK) r 2 (16QAM) b 1 b 0 =11: M 1  R  M 2 a 1 a 0 =01: M 2  R  M 1 b1b0b1b0 a1a0a1a0 b1b0b1b0 a1a0a1a0

7. Tang et al. Slide 7 System Model (FRNC) A network with a relay R and n nodes M i –n flows: each node starts a flow with another node –Packets of each flow are forwarded by R Two stages: Multiple access stage; Broadcast stage (NC) This paper: realize full-rate in the broadcast stage –Use the highest rate of all links simultaneously Assumption –(i) There are enough data for each flow to transfer –(ii) The a priori information is available (each node overhears all necessary packets) –(iii) the relay node knows the CSI of all links Special case: n=2 M1M1 M2M2 R M3M3 P2P2 P3P3 P1P1 M1M1 M2M2 RM3M3 M4M4 P1P1 P2P2 P3P3 P4P4 Special case: n=4 A network with a relay and n nodes Special case: n=3 M1M1 RM2M2 P1P1 P2P2 R M1M1 M2M2 MjMj MkMk MnMn MiMi … … …

8. Tang et al. Slide 8 NC Transmission At Relay Post-COD MOD ㊉ P 1,U =10 P n,C =11100010 P ∑ =P 1 ㊉ … ㊉ P n =00010001 At relay R Frame … CH-COD P 1,C =1101 P n,U =1101 P 1 =11110011 P n =11100010 for M 1 for M n x ∑ =(S 1 S 1 ) 16QAM Transmit a number of symbols –r 1 ≤r 2 ≤ … ≤r n –Re-framing (N*r i ) Use different constellations together –Post-COD is added to nest low level constellation inside high level constellation E.g., QPSK inside 16QAM –Select a subset of high level constellation points as the low level constellation E.g, 4 16QAM points for QPSK Key point 1: retain min-distance of low-level constellation Key point 2: demodulate the signal (modulated with high level constellation) using low level constellation M1M1 M2M2 R c 1 =1/2, m 1 =2 (QPSK) r 1 = c 1 *m 1 =1bit/sym N* r 1 =2bits/frame c 2 =1/2, m 2 =4 (16QAM) r 2 = c 2 *m 2 =2bit/sym N*r 2 =4bits/frame Frame Length: N = 2 symbols QPSK 16QAM

9. Tang et al. Slide 9 Nesting QPSK inside 16QAM At receiver M 1, constellation for b 1 b 0 ( a 3 a 2 a 1 a 0 =1110 known a priori) 0000 ㊉ 1110 = 1110 => S B0 0011 ㊉ 1110 = 1101 => S B1 1100 ㊉ 1110 = 0010 => S B2 1111 ㊉ 1110 = 0001 => S B3 M1M1 RM2M2 T 3 :P 1 ㊉ P 2 r 1 (QPSK) r 2 (16QAM) b1b1b0b0b1b1b0b0 a3a2a1a0a3a2a1a0 S 0 : 0000S 4 : 0100 S 1 : 0001S 5 : 0101 S 3 : 0011S 7 : 0111 S 2 : 0010S 6 : 0110 S 12 : 1100 S 13 : 1101 S 15 : 1111 S 14 : 1110 S 8 : 1000 S 9 : 1001 S 11 : 1011 S 10 : 1010 00xx (-0.948) 01xx (-0.316) 11xx (0.316) 10xx (0.948) xx10 (0.948) xx11 (0.316) xx01 (-0.316) xx00 (-0.948) P 2,C =11100010P 1,C =1101 P 1 =11110011P 2 =11100010 P 1,C P 2,C S B3 : 11 00xx (-0.948) 01xx (-0.316) 11xx (0.316) 10xx (0.948) xx10 (0.948) xx11 (0.316) xx01 (-0.316) xx00 (-0.948) x ∑ =(S 1 S 1 ) 16QAM P ∑ =P 1 ㊉ P 2 =00010001 00 01 10 11 b1b0b1b0 S B2 : 10 S B1 : 01 S B0 : 00 QPSK constellation under given a priori info (a 3 a 2 a 1 a 0 =1110) Post-COD: simple repetition for this example P 1,C P1P1 P2P2 At relay R

10. Tang et al. Slide 10 NC Reception At Node NC-DEC CH-DEC P 2, …, P n a priori info P2㊉…㊉PnP2㊉…㊉Pn DEMOD CH-DEC P 1, …, P n-1 a priori info P 1 ㊉ … ㊉ P n-1 DEMOD ㊉ ㊉ NC-DEC … P ∑ =00010001 x ∑ =(S 1 S 1 ) 16QAM P n,C =11100010 P n,U =1101 x 1 =(S 3 S 1 ) QPSK P 1,C =1101 P 1,U =10 s 1 (t)s n (t) for M 1 for M n a priori info a 3 a 2 a 1 a 0 QPSK constellation a 3 a 2 a 1 a 0 ㊉ b 1 b 1 b 0 b 0 0000(S 0, S 3, S 12, S 15 ) 16QAM 0001(S 1, S 2, S 13, S 14 ) 16QAM 0010(S 2, S 1, S 14, S 13 ) 16QAM 0011(S 3, S 0, S 15, S 12 ) 16QAM 0100(S 4, S 7, S 8, S 11 ) 16QAM 0101(S 5, S 6, S 9, S 10 ) 16QAM 0110(S 6, S 5, S 10, S 9 ) 16QAM 0111(S 7, S 4, S 11, S 8 ) 16QAM 1000(S 8, S 11, S 4, S 7 ) 16QAM 1001(S 9, S 10, S 5, S 6 ) 16QAM 1010(S 10, S 9, S 6, S 5 ) 16QAM 1011(S 11, S 8, S 7, S 4 ) 16QAM 1100(S 12, S 15, S 0, S 3 ) 16QAM 1101(S 13, S 14, S 1, S 2 ) 16QAM 1110(S 14, S 13, S 2, S 1 ) 16QAM 1111(S 15, S 12, S 3, S 0 ) 16QAM (S 0, S 1, S 2, S 3 ) QPSK M1M1 M2M2 R c 1 =1/2, m 1 =2 (QPSK) r 1 = c 1 *m 1 =1bit/sym N* r 1 =2bits/frame c 2 =1/2, m 2 =4 (16QAM) r 2 = c 2 *m 2 =2bit/sym N*r 2 =4bits/frame Network decoding is realized by modulation constellation conversion b 1 b 0 : (00, 01,10, 11) =11110011 =11100010

11. Tang et al. Slide 11 Discussion What is the min-distance of low level constellation, when nested inside a high level constellation? –Remain the same or decrease a little Potential SNR loss in constellation conversion. ConversionMin dist (derived /std)SNR loss QPSK  BPSK2/20dB 16QAM  QPSK(0.6325*2)/1.414-0.97dB 64QAM  16QAM(0.3086*2)/0.6325-0.21dB 256QAM  64QAM(0.1534*2)/0.3086-0.05dB S B3 : 11 00xx (-0.948) 01xx (-0.316) 11xx (0.316) 10xx (0.948) xx10 (0.948) xx11 (0.316) xx01 (-0.316) xx00 (-0.948) S B2 : 10 S B1 : 01 S B0 : 00 S 0 :00 S 1 : 01S 3 : 11 S 2 : 10 0x (-0.707) 1x (0.707) x1 (0.707) x0 (-0.707) d derived d std

12. Tang et al. Slide 12 A Simple Comparison Comparison over the broadcast channel –DecFwd: r 1 /2+r 2 /2 –NetCod (min rate): min(r 1,r 2 )*2 –FRNC (full rate): r 1 +r 2 #transmitted bits calculated with frame length N=2 Timerate# transmitted bits DecFwdr 1 /2+r 2 /23 NetCod (min rate)min(r 1,r 2 )*24 FRNC (full rate)r 1 +r 2 6 M1M1 M2M2 R c 1 =1/2, m 1 =2 (QPSK) r 1 = c 1 *m 1 =1bit/sym N* r 1 =2bits/frame c 2 =1/2, m 2 =4 (16QAM) r 2 = c 2 *m 2 =2bit/sym N*r 2 =4bits/frame

13. Tang et al. Slide 13 Simulation Evaluation Evaluating performance of the broadcast channel (forwarding) Frame length: N=4800 symbols 10 rates (#modulation level * 2 coding rate) –Coding rate: 1/2, 2/3, 3/4; 4-state RSC (1, 5/7) –Modulation: BPSK, QPSK, 16QAM, 64QAM, 256QAM (802.11a except last one) Independent block Rayleigh fading Comparison: DecFwd, NetCod [3], NCSched [8], iPack [12], FRNC M1M1 M2M2 R d M1R d M1M2 d M1R /d M1M2 NetCod: total throughput reaches maximum when R lies in the middle, and decreases otherwise iPack: has similar throughput as NetCod when R lies in the middle FRNC: outperforms iPack/NetCod even when R lies in the middle due to the effect of fading Throughput gain of FRNC against iPack reaches the max value 24% when the normalized distance equals 0.3 Two-way relay

14. Tang et al. Slide 14 Simulation Evaluation General relay scenario with multiple nodes Same setting as two way relay except the topology DecFwd transmits in a TDMA manner. Therefore, it cannot benefit from the increase in flows NetCod, NCSched and FRNC all benefit from the increase in flows more or less. Due to the different capability in handling rate mismatch, the slopes of three curves differ greatly. Special case: n=2 M1M1 M2M2 R M3M3 P2P2 P3P3 P1P1 M1M1 M2M2 RM3M3 M4M4 P1P1 P2P2 P3P3 P4P4 Special case: n=4 Special case: n=3 M1M1 RM2M2 P1P1 P2P2

15. Tang et al. Slide 15 Conclusion Re-interpretation of network coding in the modulation level –  Get the reason of rate mismatch Our proposal: full rate network coding (FRNC) –Use the highest rate of all links simultaneously Simulation evaluation –The proposal outperforms the state-of-the-art works, like NCSched [8], iPack [12], In the future we will consider the limitation of constellation size & general post-coding