Applications of low density party check codes to data compression with distortion

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A LPDC(low density parity check) code is an error correcting code that was first proposed by Gallager in 1962. Recently, BP(belief propagation) or other repeating decoding algorithms become applicable to the LDPC codes by rapid growth of computer power. In this research, we applied the LODC codes to data compression with distortion, and evaluated the performance.In 2002, we proposed an encoding algorithm to apply the LODC codes to data compression with distortion. Furthermore, we proved that there exits a LODC codes that can attain the theoretical optimal rate, i.e., rate-distortion function. In 2003, we improved the proof and published the results in the IEEE transactions on Information Theory. In the coding theorem, it is shown that if column weight t in the parity check matrix of a LODC codes satisfies t=O(log n) for code length n, the code can attain the rate-distortion function asymptotically. Furthermore, if t=O(n), then it converge to the rate-distortion function exponentially.We also show by simulation that the BP algorithm of LPDC codes for error correcting cannot attain a good performance in the case of rate-distortion coding.