Iterative Decoding for Sudoku and Latin Square Codes

This paper presents a new class of q-ary erasure-correcting codes based on Latin and Sudoku squares of order q, and an iterative decoding algorithm similar to the one used for the Low Density Parity Check code. The algorithm works by assigning binary variables to the q-ary values, and by generalizing the definition of parity check operation to represent the constraints that define the Latin and Sudoku squares.