An investigation of SUDOKU-inspired non-linear codes with local constraints

TL;DR

This paper explores SUDOKU-inspired non-linear codes with local constraints, introducing new decoding methods, a universal encoder, and analyzing their asymptotic performance through simulations.

Contribution

It presents novel decoding algorithms, a universal encoder, and performance insights for codes based on local permutation constraints inspired by SUDOKU.

Findings

Belief propagation decoding involves permanent computations.

Trellis-based methods improve permanent calculations.

Simulation results demonstrate the effectiveness of the proposed codes.

Abstract

Codes with local permutation constraints are described. Belief propagation decoding is shown to require the computation of permanents, and trellis-based methods for computing the permanents are introduced. New insights into the asymptotic performance of such codes are presented. A universal encoder for codes with local constraints is introduced, and simulation results for two code structures, SUDOKU and semi-pandiagonal Latin squares, are presented.