Density Evolution Technique for LDPC Codes in Slepian-Wolf Coding of Nonuniform Sources

This paper attempts to examine the optimality of LDPC codes for compression of nonuniform source with Slepian-Wolf coding using density evolution technique. The primary goal is to evaluate the performance of LDPC codes with reference to turbo codes (in SF-ISF setup). The appreciable difference between LDPC and turbo codes is also discussed in this paper. The threshold values obtained from the density evolution technique indicate that the conditional entropy H(X/Y) is nearly constant with source distribution. This feature is useful in calculating the threshold values for any given source distribution analytically. This special feature is true for only LDPC codes. Several well known LDPC codes, both regular and irregular are critically analyzed using density evolution technique. This analysis reveals that the capacity approaching LDPC codes with respect to error correction codes do indeed approach the Slepian-Wolf bound for nonuniform sources as well. The threshold values show that the nonuniform source can be compressed to near about 0.01bits/sample away from Slepian-Wolf bound even for highly decorrelated side information.