Implementation Of Lossy Source Coding Based On LDGM Codes

On the basis of the Shannon’s third theorem, lossy source coding is one of the hot topics in source coding. Quantization technology is a common method of lossy source coding. Many researchers have proposed many quantization algorithms which are widely used in many fields up to now. However, these algorithms can’t meet the low encoding and decoding complexity and good rate distortion performance conditions simultaneously. Low Density Generator Matrix(LDGM)codes can encode and decode data with lower complexity. So the research on LDGM codes quantization algorithm is of significant theoretic and practical value. In this paper, after analyzing LDGM codes and quantization principle based on LDGM codes, we choose three quantization algorithms to achieve the source compression based on LDGM codes and test rate-distortion performance of those algorithms. There are all research of this paper as follows:(1) In order to get good LDGM codes, we choose PEG algorithm to construct the generator matrix of irregular LDGM codes. In this paper, we use row and column of generator matrix and degree distributions as inputs of this algorithm and improve statistical independence of message between different nodes by increasing the length of ring of factor graph, thereby ensuring encoding accuracy.(2) A quantization system module based on LDGM codes is designed. In the LDGM compression module of this system, we choose message-passing decimation algorithm, belief propagation soft-decimation algorithm and Bias Propagation(BiP) algorithm to achieve mapping from source sequence to compressed sequence.(3) Random sequence is generated to test the rate-distortion performance of message-passing decimation algorithm, belief propagation soft-decimation algorithm and Bias Propagation(BiP) algorithm. In the test, we analyze the influence of different parameters on the performance of BiP algorithm and get best values of those parameters, and compare it with message-passing decimation algorithm, belief propagation soft-decimation algorithm and Shannon limit with the best values. The experimental results show that the bit error rate of BiP algorithm is 0.0002 higher than message-passing decimation algorithm, 0.0035 lower than belief propagation soft-decimation algorithm and 0.006 higher than Shannon limit with source length is 10000. The bit error rate of BiP algorithm is 0.007 higher than Shannon limit with source length is 5000 and 0.0112 higher than Shannon limit with source length is 2000. The experimental results show that BiP algorithm can reach good rate-distortion performance.