CRC-Aided Guessing Codeword Decoding for Short Blocklength Codes

In the short blocklength regime, guessing codeword decoding (GCD) can approach maximum-likelihood (ML) decoding performance as the number of guesses increases. However, this comes at the cost of potentially prohibitive decoding complexity. To address this issue, we propose the cyclic redundancy check (CRC)-aided GCD (CRC-GCD), in which a carefully chosen number of CRC bits is appended to the information block and CRC checking is embedded into the guessing process to screen candidates and reduce unnecessary re-encoding. Specifically, we use the guessing codeword decoding (GCD) to exploit the CRC constraint to eliminate invalid candidates before re-encoding. We analyze the complexity of CRC-GCD to guide the selection of CRC length, and further optimize the generator polynomial of CRC when its length is given. We prove that, for a wide range of information lengths, the decoding complexity of CRC-GCD is lower than that of GCD. Extensive simulation results are presented to show that the optimized CRC-GCD achieves substantial reductions in average decoding complexity-approximately 44.5% for Reed-Muller (RM) codes and 66.3% for random linear codes (RLC) at E b /N0 = 5 dB-with negligible performance loss. These results demonstrate that CRC-GCD is a practical and competitive decoding method for short blocklength codes.