Local Constraint-Based Ordered Statistics Decoding for Short Block Codes

Abstract

This paper is concerned with a search-numberreduced 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.

Soft Decision Decoding with Cyclic Information Set and the Decoder Architecture for Cyclic Codes

“…In order to eliminate the burden of identifying the MRB, many efforts have been paid to reduce the complexity and some significant progress has been achieved [17]. The main ideas of the existing improved OSD algorithms include skipping and/or discarding unlikely test patterns to avoid unnecessary calculations [18][19][20][21][22][23][24][25][26]. A double re-encoding technique was proposed in [27].…”