A coding theorem for lossy data compression by LDPC codes

Recently, low density parity check (LDPC) codes have been studied actively because of the high performance of error correction. Many previous researches showed that LDPC codes can attain near the Shannon limit by iterative decoding with belief propagation. On the other hand, it is well known that channel coding can be considered as the dual problem of lossy source coding in the rate-distortion theory, and a good error correcting code can be used for efficient lossy data compression. In this paper, we show that LDPC codes can also attain the rate-distortion function asymptotically for the same source.