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

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

3 Gaussian case (DPC)  Channel description (Dirty paper coding - Costa 1983)  Coding 

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

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

6 Problem statement in MIMO BC : Decoder #1 Decoder #K : r 1 antennas r K antennas Y1Y1 YKYK : Encoder W1W1 WKWK t antennas X p(y|x,H) H H1H1 HKHK

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 DPC and MIMO BC : Decoder #1 Decoder #K : r 1 antennas r K antennas Y1Y1 YKYK : Encoder W1W1 WKWK t antennas X p(y|x,H) H H1H1 HKHK

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

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 Structure of DPC schemes for Gaussian MIMO BCs  Outer encoders  Tomlinson Harashima precoder (THP)  Scalar Costa’s scheme (SCS)  Trellis coded quantization (TCQ) + turbo  Nested lattices  Encoder structure Inner Encoder Outer Encoder : W1W1 WKWK X H  Outer encoders : Linear  Pre-equalizers: MF, ZF, MMSE  ZF-DPC  MMSE-DPC

13 Structure of DPC schemes for Gaussian MIMO BCs  Encoder structure

14 Comparison of outer coders

15 Inner coding  Comments  Inner coding  space-time coding or beamforming  Inner + outer coding  implements a good multiple access scheme  Received signal structure  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)

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 :  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 Numerical Method to compute Sum Rate Water-Filling

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

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

22 Overall performance (1/2) Degraded channel (No need to inner coder) Application de TCQ pour un BC scalaire dégradé 2 utilisateurs x2x2 y2y2 Viterbi Decoder y1y1 TCQ u1u1 x1x1 u2u2 x z1z1 z2z2 0 Viterbi Decoder

23 Overall performance (2/2)