LDPC Codes for Information Embedding and LossyDistributed Source Coding

Mina SartipiDepartment of Computer Science and Engineering

University of Tennessee at ChattanoogaChattanooga, TN 37403 − 2598E-mail: mina-sartipi@utc.edu

Inspired by our recently proposed constructive framework for the lossy distributed source coding withside information available at the decoder, we propose a framework for information embedding with sideinformation available at the encoder. Our proposed method is based on sending parity bits using LDPCcodes. The process of embedding information M in the host signal Y with length k is shown in Fig. 1. As

BSC(p)Yd YdY ChannelDecoder

M

^Yd

M

ChannelDecoder

Fig. 1. Embedding information M is the host signal Y .

shown in Fig. 1, the signal Y is mapped to the composite signal Yd using the side information M availableat the encoder. This mapping is done such that no serious degradation is caused to Y , ρ(Yd, Y ) ≤ d, andthe composite signal is robust against deliberate attacks, which are modeled by BSC(p) in Fig. 1. Thereceiver recovers M from Yd.

To generate Yd, we propose to use a systematic LDPC code with the generator matrix G = [I|P1|P2],where I is the identity matrix of dimension k(1− h(d))× k(1− h(d)). We assume that Yd is a codewordof the matrix G generated from information message yd of length k(1 − h(d)), where ydP1 = M andydP2 = 0. Using these assumptions on yd and the fact that ρ(Yd, Y ) ≤ d, Yd is found by using the LDPCdecoder corresponding to the code G. It can be easily shown that the procedure explained above resultsin an embedding rate of h(d) − h(p), which is known as Gelfand-Pinsker limit.

We further provide a detailed design procedure for the LDPC code that guarantees performance closeto the Gelfand-Pinsker limit. The parity-check matrix associated with the generator matrix G described

above is of the form H =

[P T

1

P T2

∣∣∣∣∣I]

. First, we design the equivalent LDPC code with parity-check matrix

H =[

C1

C2

∣∣C3

], then using Gaussian elimination an equivalent parity-check matrix in the systematic form

can be derived. The conditions that matrix H needs to satisfy are as follows:1) The submatrix C2 must be designed such that Yd can be recovered from Yd.2) The matrix H must be designed such that Y can be mapped to Yd.

Considering the above two conditions, we designed LDPC codes and measured their performance fordifferent lengths. The simulation results show that the gap from the Gelfand-Pinsker theoretical limits fora code of length 952 is 0.2 and the gap decreases as code length increases.

2010 Data Compression Conference

1068-0314/10 $26.00 © 2010 IEEE

DOI 10.1109/DCC.2010.87

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