Representative OSD with Local Constraints of CA-Polar Codes

In this paper, we propose an algorithm to transform a generator matrix of a linear block code into a minimum weight staircase generator matrix (MWSGM). This allows us to apply the representative ordered statistics decoding with local constraints (LC-ROSD) algorithm to cyclic redundancy check (CRC) aided polar (CA-polar) codes. Distinguished from the conventional ordered statistics decoding (OSD), the LC-ROSD implements parallel Gaussian elimination (GE) for MWSGM instead of serial GE for a general matrix, potentially reducing the decoding latency. Numerical results show that the performance of 5G CA-polar codes under LC-ROSD is better than that of CRC aided successive cancellation list (CA-SCL) decoding and can approach the corresponding maximum likelihood (ML) lower bounds at different code rates. The numerical results also show that the LC-ROSD with MWSGM has lower decoding complexity than the CA-SCL decoding in the high signal-to-noise ratio (SNR) region.