Partially Constrained GRAND of Linear Block Codes

This paper is concerned with a search-number-reduced guessing random additive noise decoding (GRAND) algorithm for linear block codes, called partially constrained GRAND (PC-GRAND). In contrast to the original GRAND, which guesses error patterns without constraints, the PC-GRAND guesses only those error patterns satisfying partial constraints of the codes. In particular, the PC-GRAND takes partial rows of the parity-check matrix as constraints for generating candidate error patterns and the remaining rows as checks for validating the candidates. The number of searches can be reduced when the serial list Viterbi algorithm (SLVA) is implemented for searching over a trellis specified by the partial parity-check matrix. This is confirmed by numerical results. Numerical simulations are also provided for comparison with other decoding algorithms. The parallel implementation of PC-GRAND is also presented in this paper.