Tree-Based Construction of LDPC Codes

TL;DR

This paper introduces a novel tree-based method for constructing LDPC codes that achieve optimal pseudocodeword weight and exhibit strong iterative decoding performance, utilizing Latin squares and finite geometry concepts.

Contribution

The paper proposes a new construction technique for LDPC codes using enumerated trees and Latin squares, including methods for specific degrees and connections to finite geometry.

Findings

Codes with minimum pseudocodeword weight equal to minimum distance

Construction methods for degrees d=p^s and d=p^s+1

Codes perform well with iterative decoding

Abstract

We present a construction of LDPC codes that have minimum pseudocodeword weight equal to the minimum distance, and perform well with iterative decoding. The construction involves enumerating a d-regular tree for a fixed number of layers and employing a connection algorithm based on mutually orthogonal Latin squares to close the tree. Methods are presented for degrees d=p^s and d = p^s+1, for p a prime, -- one of which includes the well-known finite-geometry-based LDPC codes.