Efficient Encoding Algorithm of Binary and Non-Binary LDPC Codes Using Block Triangulation

TL;DR

This paper introduces an efficient encoding algorithm for binary and non-binary LDPC codes that reduces complexity by transforming the parity-check matrix into a block triangular form, enabling faster encoding especially for non-binary cycle codes.

Contribution

The paper presents a novel encoding algorithm that transforms the parity matrix into a block triangular form, significantly reducing encoding complexity for LDPC codes.

Findings

Lower encoding complexity compared to existing methods

Linear time encoding for non-binary cycle codes

Effective transformation of parity matrices into block triangular form

Abstract

We propose an efficient encoding algorithm for the binary and non-binary low-density parity-check codes. This algorithm transforms the parity part of the parity-check matrix into a block triangular matrix with low weight diagonal submatrices by row and column permutations in the preprocessing stage. This algorithm determines the parity part of a codeword by block back-substitution to reduce the encoding complexity in the encoding stage. Numerical experiments show that this algorithm has a lower encoding complexity than existing encoding algorithms. Moreover, we show that this algorithm encodes the non-binary cycle codes in linear time.