On the Designs and Challenges of Practical Binary Dirty Paper Coding

Transcription

1 On the Designs and Challenges of Pratial Binary Dirty Paper Coding 04 / 08 / 2009 Gyu Bum Kyung and Chih-Chun Wang Center for Wireless Systems and Appliations Shool of Eletrial and Computer Eng.

2 Outline Introdution General Framework of Binary DPC Binary DPC-The Proposed Pratial System The system model Deoding in the Fator Graph Code Design Choose the system parameters Code optimization Simulation and Disussions Conlusion 2

3 Introdution Multi-user MIMO broadast model y = H x + H x + n M i i 1 i= 2 d H 1 11x1 ENC M H1ixi n1 i= 2 y 1 Why dirty paper oding (DPC)? Eliminating inter-user interferene (IUI) Alternative approah: linear proessing (away from the apaity) Costa s proof (Costa 83) Footstone of theoretial studies of the Gaussian MIMO broadast hannel (Caire et al. 03) 3

4 General Framework of Binary DPC DPC enoder sends the transmitted signal x, a funtion f ( ds, ) of the interferene s and information data d y = x+ s+ n The goal of DPC is to optimize the transmission rate subjet to a normalized power onstraint on x. W R Interferene s d Enoder BSC( p) Deoder x= f ( d, s) y ˆd 4

5 Ahieving DPC apaity: Random binning Nonausal side information (Gel fand and Pinsker 80) C = max I( U; Y) I( U; S). puxs Generate ( ( ; ) ) 2 N I U Y δ sequenes, divide these into bins R is hosen to be less than IUY ( ; ) IUS ( ; ) ε, eah bin has ( ( ; ) ) sequenes 2 N I U S ε Enoder finds a sequene u whih is the losest to s based on d and sends x whih is a funtion of u and s. Deoder looks for a sequene u s.t. u and y are the losest and identifies the bin whih inludes u. (, ) [ ] U 2 NR X Y S U 5

6 Coset-based binning C : the quantization ode and the information 0, C1 bearing ode d is mapped to, + C forms a oset (a bin) Given s, the enoder finds 0 suh that + in the 1+ C0 bin is the losest to s The transmitted signal x is s The deoder finds and 1 suh that is the losest to y. For a pratial implementation, if 0 and 1 are uniform, then no bit-based message-passing deoder an extrat any information from

7 Superpostion-oding-based (Bennatan et al. 06) Either 0 or 1 has non-uniform a priori distribution to initialize iterative deoding Nonbinary low-density parity-hek (LDPC) odes The normalized Hamming weight σ of GF( q ) LDPC ode an only ahieve σ Symbol mapper a nonlinear ode σ = = 1, 2,, ( q 1) q q q X S U nonuniform C

8 The proposed system Coset-based binning Initialization problem Edge erasing with binary LDPC odes to initialize iterative deoding X S U uniform C 1 Code optimization Density evolution (DE), the extrinsi information transfer (EXIT) hart

9 System model Random interleaver to redue the dependene is puntured by e and is padded with zeros. Viterbi deoder hooses 0 suh that 0 + ( 1) p is losest to 1 s y = x+ s+ n= 0 + ( 1) p + n 9

10 Deoding in the Fator Graph Iterative deoding between the BCJR and LDPC deoders Set LLR values at puntured positions using y = + n BCJR deoder - Log MAP After BCJR deoding, the extrinsi information in the non-puntured part is delivered to LDPC deoder. LDPC deoding is performed with the reeived bits and the extrinsi LLR information Continue iterative deoding 0 10

11 System parameters BSC with p and weight onstraint W are given and design parameters are and R R0 1 R0 and R1 W and p The proposed sheme Superposition (Bennatan et al.) No onstraint R > 1 hw ( ), R < hw ( ) h( p) 0 1 W = σ (1 p) + p(1 σ ) q No onstraint σ = 1/q to (q-1)/q To flexibly support different W values, very high-order GF(q) has to be used - inreases omplexity Our system is flexible and an easily handle different weight onstraints W using edge erasing and binary LDPC odes. 11

12 Code optimization The EXIT hart Use ol and il as the input and the output Assuming ol (il resp.) is always Gaussian distributed input with mean and variane ( μ, 2μ ) for BCJR (LDPC) The mutual information of the output LLR messages is obtained by I( X; Y) = h( X) h( X Y) = 1 h( X Y) + m e + 1 = 1 log 2 P( m X = 0) dm m e where m denotes the LLR messages, that is, m = log 2( Y X = 0) log ( Y X = 1) 2 12

13 How to hoose e Estimate the threshold * p By seleting the largest p value - two urves do not ross eah other Optimize the e value * p * Optimize p and e iteratively Given, hoose an e value - the two urves are the farthest apart 13

14 Code design for LDPC ode The joint use of DE and the EXIT hart Reord the distributions of il, use the pmfs as an input of DE Perform DE iterations, obtain the distribution of ol By omputing the mutual information of ol, use the EXIT urve of BCJR to find the pmf of il Given a degree distribution, hek whether the EXIT urve and DE onverge Differential Evolution 14

15 Trajetory of Monte Carlo Simulation Reord the LLR distributions under real BCJR+LDPC deoding and onvert them to the mutual information The zigzag trajetory fits the two EXIT urves well By hoosing different numbers of LDPC iterations in the initial and final stages, we an ontrol the total number of LDPC iterations to be roughly How many outer loop iteration? 15

16 Simulation and Disussions 5 Quasi-yli LDPC odes ( R 1 = 0.36, N =10 ) base matrix λ( x) = 0.53x+ 0.21x x x, ρ( x) = 0.2x + 0.8x Convolutional ode ( R 1 0 = 8 ) (2565, 2747,3311,3723, 2373,2675,3271, 2473) Performane * * p = vs p = 0.1 Our sheme have several advantages omplexity, flexibility, and effiient enoding and deoding

17 Conlusion Pratial sheme for binary dirty-paper hannels based on random binning Binary LDPC odes and edge erasing - the advantages for omplexity. Choose system parameters flexibly - important in the pratial system. Code design ombining EXIT hart and DE jointly Similar performane to that of state-of-the-art superposition-oding-based binary DPC sheme. Future researh Extend to Gaussian DPC 17