Performance Analysis and Enhancement of P-LDPC Codes for Lossy Compression of Binary Sources

Due to the duality between source coding and channel coding, high-performance channel codes are often adopted for addressing source coding problems. In this paper, we investigate the design and analysis of protograph low-density parity-check (P-LDPC) codes in lossy source coding systems. First, we propose a novel lossy source coding architecture based on P-LDPC codes, and empirically verify that although high-performance channel codes perform exceptionally well in their intended domain, they are not inherently optimal for lossy compression. To facilitate analysis, we introduce the lossy compression protograph extrinsic information transfer (LC-PEXIT) algorithm, which aids in evaluating the rate-distortion (RD) performance of P-LDPC codes. Additionally, the LC-PEXIT algorithm allows for the prediction of key parameters, such as the prior coefficient <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P</i> and the reinforcement rate <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</i>, both of which critically influence system performance. We further propose a design algorithm for lossy P-LDPC codes and provide two sets of design examples. Experimental results show strong alignment between the predicted and actual values of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</i>f, with the designed P-LDPC codes exhibiting superior RD performance compared to classical P-LDPC and state-of-the-art ultra-sparse LDPC (US-LDPC) codes. In particular, the designed P-LDPC codes over benchmark codes increases the system coding efficiency of up to approximate 70% and achieves a performance gain of 1.69 ~ 3.26 dB, making it highly effective for lossy compression applications.