Iterative Decoding for Sudoku and Latin Square Codes
نویسندگان
چکیده
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.
منابع مشابه
Search Based Weighted Multi-Bit Flipping Algorithm for High-Performance Low-Complexity Decoding of LDPC Codes
In this paper, two new hybrid algorithms are proposed for decoding Low Density Parity Check (LDPC) codes. Original version of the proposed algorithms named Search Based Weighted Multi Bit Flipping (SWMBF). The main idea of these algorithms is flipping variable multi bits in each iteration, change in which leads to the syndrome vector with least hamming weight. To achieve this, the proposed algo...
متن کاملSearch Based Weighted Multi-Bit Flipping Algorithm for High-Performance Low-Complexity Decoding of LDPC Codes
In this paper, two new hybrid algorithms are proposed for decoding Low Density Parity Check (LDPC) codes. Original version of the proposed algorithms named Search Based Weighted Multi Bit Flipping (SWMBF). The main idea of these algorithms is flipping variable multi bits in each iteration, change in which leads to the syndrome vector with least hamming weight. To achieve this, the proposed algo...
متن کاملThe Structure of Reduced Sudoku Grids and the Sudoku Symmetry Group
A Sudoku grid is a constrained Latin square. In this paper a reduced Sudoku grid is described, the properties of which differ, through necessity, from that of a reduced Latin square. The Sudoku symmetry group is presented and applied to determine a mathematical relationship between the number of reduced Sudoku grids and the total number of Sudoku grids for any size. This relationship simplifies...
متن کاملIterative Decoding of Product Block Codes based on the Least Mean Square Error Criterion
A soft-input soft-output decoder based on the least mean square error (LMSE) criterion is presented and employed for iterative decoding of product codes. The residual estimation error is derived and used for analyzing the convergence of the iterative process as well as a stopping criterion. A relation between the LMSE and the MAP decoders is also established. Simulation results are presented fo...
متن کاملFactor pair latin squares
Sudoku has risen in popularity over the past few years. The rules are simple, yet the solutions are often less than trivial. Mathematically, these puzzles are interesting in their own right. This paper will generalize the idea of a sudoku puzzle to define a new kind of n× n array. We define a latin square of order n as an n×n array where every row and every column contain every symbol 1, 2, . ....
متن کامل