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Gholam-Reza MOHAMMAD-KHANI

Codage avec Information Adjacante (DPC : Dirty paper coding) et certaines de ses applications : Tatouage (Watermarking) MIMO broadcast channels. Gholam-Reza MOHAMMAD-KHANI. Channel capacity (Gel’fand and Pinsker 1980). Gel’fand and Pinsker’s channel. Channel definition. Encoder.

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Gholam-Reza MOHAMMAD-KHANI

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  1. Codage avec Information Adjacante (DPC : Dirty paper coding) et certaines de ses applications : Tatouage (Watermarking)MIMO broadcast channels Gholam-Reza MOHAMMAD-KHANI

  2. Channel capacity (Gel’fand and Pinsker 1980) Gel’fand and Pinsker’s channel • Channel definition Encoder

  3. Channel description (Dirty paper coding - Costa 1983) • Coding Gaussian case (DPC)

  4. Channel description (Dirty paper coding - Costa 1983) Gaussian case (DPC) • Coding S   W U X Encoder

  5. Channel description (Dirty paper coding - Costa 1983) DPC Application for Watermarking • Watermarking Application : • X : Mark (Weak Signal) , S : Host (Strong Signal) , Z : Noise • Capacity Achieving for Mark Signal

  6. r1 antennas Y1 : Decoder #1 : W1 YK : X Decoder #K Encoder WK t antennas H rK antennas p(y|x,H) Problem statement in MIMO BC H1 HK

  7. Performance Criteria in BC : • Usual Criteria (Information Theory Aspects) : • Capacity Regions • Throughput (Sum Capacity) • New Criteria (Practical Aspects) : • BER Regions • Number of Satisfied Users (of Rates or of BER)

  8. Some Relateds Works : • Sato : • Upperbound for Sum Capacity of BC • - Cover [72] : • Definition of Broadcast Channels • - Weingarten & Shamai [06] : • Capacity Region of Gaussian MIMO BC • - Caire & Shamai [03] + Viswanath & Tse [03] + • Vishwanath & Goldsmith [03] + Yu & Cioffi [04]: • Achievable Throughput of Gaussian MIMO BC • DPC scheme : • Achieve Sum Capacity and Capacity Region for MIMO BC

  9. r1 antennas Y1 Decoder #1 : YK Decoder #K rK antennas DPC and MIMO BC : H1 W1 : X Encoder WK HK t antennas H p(y|x,H)

  10. Channel model and capacity region Superposition coding: One Simple Case : Gaussian SISO BC

  11. DPC vs TDMA • Theorique Comparison : • Jindal & Goldsmith [05] : • Best performance of DPC on Sum Capacity • Weingarten & Shamai [06] : • Best Performance of DPC on Capacity Region • Practical Comparison : • Belfiore [06] • Mohammad-Khani & Lasaulce [06] • Sensibility to Channel Estimation • BER Comparison

  12. Outer Encoder Inner Encoder Structure of DPC schemes for Gaussian MIMO BCs • Encoder structure W1 : X WK H • Outer encoders : Linear • Pre-equalizers: MF, ZF, MMSE • ZF-DPC • MMSE-DPC • Outer encoders • Tomlinson Harashima precoder (THP) • Scalar Costa’s scheme (SCS) • Trellis coded quantization (TCQ) + turbo • Nested lattices

  13. Structure of DPC schemes for Gaussian MIMO BCs • Encoder structure

  14. Comparison of outer coders

  15. Received signal structure Inner coding • Possible approaches • Linear precoding with successive coding using DPC as outer coding (the outer coder treats the interference) • Linear pre-equalizer with independent outer coder (the outer coder does not treat the interference) • Comments • Inner coding  space-time coding or beamforming • Inner + outer coding  implements a good multiple access scheme

  16. MMSE-DPC • Main features • Optimum in the sense of the sum-capacity • Two ways of implementing it: • Yu & Cioffi 04 (GDFE precoder) • Viswanath & Tse 03 (duality BC – MAC) • Precoding filters depend on power allocation • Coding order: no effect on sum capacity (not true for the capacity region) • Power allocation: we used the policy proposed by Boche & Jorswieck 04 (corresponding numerical algorithms converge) Numerical technique

  17. ZF-DPC • Main features • Introduced by Caire & Shamai 03 (for single-antenna receivers) • We generalized this scheme to multi-antenna receivers • Simpler than MMSE-DPC but suboptimum in terms of sum-capacity • Quasi-optimal in terms of sum-capacity, when H is full row rank • Number of served users limited to rank of H • Sensitive to coding order Waterfilling :

  18. Influence of the coding order: example • Conclusions • Coding order has no effect on sum rate for MMSE-DPC • Sum rate of ZF-DPC strongly depends on coding order • Coding order can be optimized by a greedy algorithm [Tu & Blum03] • If the coding order is not well chosen: TDMA can perform better than DPC (especially for low SNRs)

  19. Conventional pre-equalizers • Definitions • ZF : • MMSE : • MF : Water-Filling Numerical Method to compute Sum Rate • Comments • The outer coder does not help to the interference cancellation task (separate coding) • No successive coding = no coding order • Most simple schemes when the CSI is known

  20. Comparison of inner coders (1/2) Sum Rate Comparison

  21. Comparison of inner coders (2/2) Region of achieved Rate Comparison P=10dB P=7dB P=20dB

  22. Overall performance (1/2) Degraded channel (No need to inner coder) Application de TCQ pour un BC scalaire dégradé 2 utilisateurs 0 z2 y2 u2 x2 Viterbi Decoder TCQ x z1 u1 x1 Viterbi Decoder TCQ y1

  23. Overall performance (2/2)

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