Efficient Belief Propagation Polar Decoder With Loop Simplification Based Factor Graphs

The performance of belief propagation list (BPL) decoding of polar codes is related to the selection of <inline-formula><tex-math notation="LaTeX">$L$</tex-math></inline-formula> factor graphs (FGs), which have the least number of girths. However, the straightforward search of such FGs is of high complexity. To achieve good performance with reasonable complexity, we propose an efficient method to find FGs with the least number of length-12 loops in all permuted FGs. Since some length-12 loops have been destroyed by redundant decoding operations, the corresponding FGs can be simplified to different numbers of length-12 loops. Thanks to the proposed loop simplification (LS), BPL decoding is now based on more efficient FGs, resulting in better performance and lower average decoding latency than the state-of-the-art. Numerical results have shown that the performance improvement is 0.15 dB when frame error ratio (FER) is <inline-formula><tex-math notation="LaTeX">$10^{-4}$</tex-math></inline-formula>, for <inline-formula><tex-math notation="LaTeX">$(1024, 512)$</tex-math></inline-formula> codes with <inline-formula><tex-math notation="LaTeX">$L=64$</tex-math></inline-formula>.