Synchronization in Physical- Layer Network Coding

Transcription

1 Synchronization in Physical- Layer Network Coding Soung Liew Institute of Network Coding The Chinese University of Hong Kong Slides in this talk based on partial content in Physical-layer Network Coding: Tutorial, Survey, and Beyond. A 60-page monograph. ( Jan 0 Soung Liew, CUHK

2 Background First proposed in a challenge paper of Mobicom 06 [] A subfield of Network Coding with some momentum in last two years Special journal issues dedicated to the topic. Citations to-date: 500+ (Google Scholar) Fundamental impact on Communications, Information Theory, and Networking esearch. [] S. Zhang, S. C. Liew, P. P. Lam, Physical-Layer Network Coding, ACM Mobicom 006. Similar idea in [] P. Popovski and H. Yomo, The anti-packets can increase the achievable throughput of a wireless multi-hop network, ICC 006. Jan 0 Soung Liew, CUHK

3 Outline Basic idea of PNC Communication-theoretic research Information-theoretic research Network-theoretic research Conclusion Jan 0 Soung Liew, CUHK 3

4 Simplest Set-up: Two-Hop Linear Network S S Two-way elay Channel (TWC) No direct channel between nodes and. Half duplex: nodes cannot transmit and receive at the same time. What is the minimum number of time slots needed for nodes and to exchange one packet via relay node? Jan 0 Soung Liew, CUHK 4

5 Traditional Scheduling (TS) S S S S Time slot Time slot 3 Time slot Time slot 4 Transmissions non-overlapping in time Jan 0 Soung Liew, CUHK 5

6 Straightforward Network Coding (SNC) S = S S S = S S S S S = S S S = S S Time slot Time slot 3 Time slot Node uses one time slot to broadcast Transmissions by nodes and still non-overlapping Jan 0 Soung Liew, CUHK 6

7 PNC S = S S S = S S S S S = S S S = S S Time slot Time slot Transmissions by nodes and are simultaneous! Jan 0 Soung Liew, CUHK 7

8 PNC Modulation Mapping () Assume BPSK modulation S S r () t = s() t + s() t = acos( ωt) + acos( ωt) = ( a + a )cos( ωt) bit = ai = bit = 0 ai = a a aa Jan 0 Soung Liew, CUHK 8

9 PNC Modulation Mapping () a + a a a a = aa - - eception at relay Transmission by relay Jan 0 Soung Liew, CUHK 9

10 BE performance of PNC at elay BE QPSK PNC modulation Traditional network coding SN per bit (db) Jan 0 Soung Liew, CUHK 0

11 Synchronization Penalties (unchannel-coded case) () X X x[ n] x[ n+ ] x[ n] x[ n+ ] Δ y () t = x [ n] h p( t nt) + n n x [ n] h p( t ΔT nt) + w ( t) y( t) = received baseband signal pt ( ) = pulse shape Δ= symbol offset w () t = noise Jan 0 Soung Liew, CUHK

12 Synchronization Penalties (unchannel-coded case) () Assumption: Transmitters do not perform precoding to synchronize elay knows the channels h, h and symbol offset Δ Suboptimal results in [] [7] Better results in [8] [7] S. Zhang, S. C. Liew, P. P. Lam, Physical-Layer Network Coding, April 007 On the Synchronization of Physical-Layer Network Coding, IEEE Information Theory Workshop, Oct 006. [8] L. Lu, S. C. Liew, S. Zhang, Decoding Algorithm for Asynchronous Physical-Layer Network Coding, IEEE ICC Jan 0. 0 Soung Liew, CUHK

13 Synchronization Penalties (unchannelcoded case) (5) Our recent work [8] assumes oversampling and uses Belief Propagation (BP) to compute P( x[ n] x [ n] y [],..., y [N + ]) for n=,..., N h x[] h x [] Δ h x [] h x [] y [] y [] y [N + ] Two samples per symbol P( x[ n] x [ n] = x y [],..., y [N + ]) = P( x[ n], x [ n] y [],..., y [N + ]) x [ n] x [ n] = x Jan 0 Soung Liew, CUHK 3

14 Synchronization Penalties (unchannel-coded case) (6) h x [ n] h x [ n+ ] Δ h x [ n] h x [ n+ ] Tanner Graph for BP decoding of Yields exact ML decoding because of the tree structure ( N) ( N) ( N, N) ( x x y ) ( N) ( N) ( N, N) ( x x y ) ( N) ( N) ( N, N) ( x x y ) ( N) ( N) ( N, N) ( x x y ) Px ( [ n], x[ n] y[],..., y[n+ ]) Pr = 0, = 0 Pr = 0, = Pr =, = 0 Pr =, = (, ) ( ) ( ) (, ) where y N N = ( Δ )[ h x N + h x N ] + w N N ( x, ) () ( x, x ) () () Jan 0 0 Soung Liew, CUHK 4

15 Synchronization Penalties (Unchannel-coded case) (7) h x [ n] h x [ n+ ] Δ h x [ n] h x [ n+ ] BPSK results from recent work [8] Little penalty with phase and symbol asynchronies, thanks 0 0 BPSK modulated PNC to BP decoding 0 0 BPSK modulated PNC BE 0-3 BE Δ=0 and φ=0 Δ=0 and φ=π/4 Δ=0 and φ=π/ SN per bit E b /N 0 (db) Δ=0 and φ=0 Δ=0.5 and φ=0 Δ=0.5 and φ=π/4 Δ=0.5 and φ=π/ SN per bit E b /N 0 (db) Jan 0 Soung Liew, CUHK 5

16 Synchronization Penalties (Unchannel-coded case) (7) h x [ n] h x [ n+ ] Δ h x [ n] h x [ n+ ] QPSK results from recent work [8] QPSK modulated PNC QPSK modulated PNC BE db penalty here without symbol misalignment BE Symbol misalignment reduces the phase asynchrony penalty by 5 db, thanks to BP decoding Δ=0 and φ=0 Δ=0 and φ=π/8 Δ=0 and φ=π/ SN per E /N (db) b bit 0 E b /N 0 (db) (a) Δ=0 and φ=0 Δ=0.5 and φ=0 Δ=0.5 and φ=π/8 Δ=0.5 and φ=π/ SN per E /N (db) b bit 0 E b /N 0 (db) (b) [9] Y. Hao, D. Goeckel, Z. Ding, D. Towsley, K. K. Leung, Achievable ates of Physical Layer Network Coding Schemes on the Exchange Channel, Milcom 007 Jan 0 Soung Liew, CUHK 6 (This paper mentions penalty of 6dB for phase asynchrony in QPSK PNC)

17 Certainty Propagation with Symbol Misalignment ( + j, + j) 3 Constellation maps of QPSK AUPNC X A X B e jπ/4 X A +X B e jπ/4 h x [ n] h x [ n+ ] Same-colored diamonds mapped to the same XO PNC symbol. The outer 8 constellation points are separated further apart than the inner 8 constellation points. Δ h x [ n] h x [ n+ ] ( + j, + j) ( j, + j) 0 ( j, + j) Jan 0 Soung Liew, CUHK 7

18 Certainty Propagation with Symbol Misalignment Diversity: it pays to have the information of a source symbol straddle in two constellation points. Chain action : it pays even more to have symbols chained together in successive constellation points. bad bad bad good ( + j, + j) 3 Constellation maps of QPSK AUPNC (i) X A X B e jπ/4 X A +X B e jπ/4 ( + j, + j) h x h x h x ( n) ( n+ ) ( n+ ) Δ h x h x + ( n) ( n ) (ii) (i) ( j, + j) 0 - (ii) ( j, + j) - Certainty propagation thanks to BP Jan 0 Soung Liew, CUHK 8

19 How to Incorporate Channel Coding? Two variants: (i) end-to-end; (ii) link-bylink Focus on Link-by-link Jan 0 Soung Liew, CUHK 9

20 Channel-coded PNC Multiaccess (Uplink) Phase: X =C(S ) X =C(S ) eception at relay ( Δ= 0 case): y [ n] = h x [ n] + h x [ n] + w [ n] n=,..., N Jan 0 Soung Liew, CUHK 0

21 Link-by-Link Channel-coded PNC () Conceptually, channel-coded PNC consists of two parts: (i) Map Y S = S S = ( s[] s[],..., s[ M] s[ M]) ) (ii) Compute X = C( S ) This is similar to conventional channel coding This mapping involves both Channel decoding and Network Coding. Input is N samples, output is M < N symbols when Key issue: how to do CNC(.)? Jan 0 Soung Liew, CUHK

22 Link-by-Link Channel-coded PNC (9) esults of JT CNC for BPSK With channel coding, phase asynchrony results in better performance when symbols are aligned 0 0 Channel-coded BPSK PNC Phase does not play a big role when symbols are misaligned. 0 0 Channel-coded BPSK PNC BE 0-3 BE Δ=0 and θ=0 Δ=0 and θ=π/4 Δ=0 and θ=π/.5.5 SN per bit E b /N 0 (db) Δ=0 and θ=0 Δ=0.5 and θ=0 Δ=0.5 and θ=π/4 Δ=0.5 and θ=π/.5.5 SN per bit E b /N 0 (db) Jan 0 Soung Liew, CUHK

23 Link-by-Link Channel-coded PNC (0) esults of JT-CNC for QPSK 0 0 Channel-coded QPSK PNC 0 0 Channel-coded QPSK PNC BE 0-3 BE Δ=0 and φ=0 Δ=0 and φ=π/8 Δ=0 and φ=π/4.5.5 SN per bit E b /N 0 (db) Δ=0 and φ=0 Δ=0.5 and φ=0 Δ=0.5 and φ=π/8 Δ=0.5 and φ=π/4.5.5 SN per bit E b /N 0 (db) Jan 0 Soung Liew, CUHK 3