Variable length lossy coding using an LDPC code

LDPC codes initially studied for channel coding can be applied to source coding, and Miyake-Muramatsu showed theoretically that the rate-distortion function can be achieved asymptotically by using LDPC codes for any stationary memoryless finite source. In their scheme, a source sequence is first vector-quantized by using an LDPC matrix and then it is compressed losslessly by another LDPC matrix. So, their scheme is fixed length coding. Unfortunately, it is not shown that their scheme can attain a good performance practically. In this paper, we propose a new variable length coding scheme, which uses linear programming for vector-quantization and arithmetic coding with probability estimated by belief propagation for lossless coding. The proposed variable length lossy coding can attain the rate-distortion function asymptotically. Furthermore, it can practically attain a performance considerably better than the so-called time sharing bound of the rate-distortion function.