Locally Constrained Guessing Codeword Decoding of Short Block Codes

This paper is concerned with a universal guessing codeword decoding (GCD) of linear block codes, referred to as locally constrained GCD (LC-GCD), which does not require the online Gaussian elimination (GE). Distinguished from the GCD algorithm, the proposed LC-GCD queries the partial error patterns using the serial list Viterbi algorithm (SLVA) over a trellis specified by a local parity-check matrix, typically reducing the number of queries. Moreover, we introduce a parallel implementation of the LC-GCD algorithm to reduce decoding latency without compromising performance. Numerical results show that the LC-GCD requires a fewer number of queries than the GCD without performance loss, indicating a lower complexity in general. The comparisons with other decoding algorithms are also provided to demonstrate the potential advantage in complexity of the LC-GCD.