1-State Error-Trellis Decoding of LDPC Convolutional Codes Based on Circulant Matrices

TL;DR

This paper introduces a 1-state error-trellis decoding method for LDPC convolutional codes that simplifies decoding complexity while maintaining optimal error correction, especially using circulant matrices with monomial entries.

Contribution

The paper proposes a novel 1-state error-trellis decoding approach that reduces complexity and applies it to circulant matrices with monomial entries, achieving efficient decoding.

Findings

Decoding complexity is similar to conventional methods.

A 1-state error trellis can be constructed using circulant matrices.

Decoding complexity is reduced through a simplified method.

Abstract

We consider the decoding of convolutional codes using an error trellis constructed based on a submatrix of a given check matrix. In the proposed method, the syndrome-subsequence computed using the remaining submatrix is utilized as auxiliary information for decoding. Then the ML error path is correctly decoded using the degenerate error trellis. We also show that the decoding complexity of the proposed method is basically identical with that of the conventional one based on the original error trellis. Next, we apply the method to check matrices with monomial entries proposed by Tanner et al. By choosing any row of the check matrix as the submatrix for error-trellis construction, a 1-state error trellis is obtained. Noting the fact that a likelihood-concentration on the all-zero state and the states with many 0's occurs in the error trellis, we present a simplified decoding method based on a 1-state error trellis, from which decoding-complexity reduction is realized.