Terminated LDPC Convolutional Codes with Thresholds Close to Capacity

TL;DR

This paper analyzes LDPC convolutional codes with permutation matrix-based parity-checks, showing they achieve thresholds close to channel capacity due to their structured irregularity, which improves decoding performance.

Contribution

It introduces an ensemble of LDPC convolutional codes with permutation matrices and demonstrates their superior thresholds over block codes through density evolution analysis.

Findings

Structured irregularity enhances decoding thresholds.

Convolutional codes outperform block codes in threshold performance.

Thresholds approach channel capacity with the proposed ensemble.

Abstract

An ensemble of LDPC convolutional codes with parity-check matrices composed of permutation matrices is considered. The convergence of the iterative belief propagation based decoder for terminated convolutional codes in the ensemble is analyzed for binary-input output-symmetric memoryless channels using density evolution techniques. We observe that the structured irregularity in the Tanner graph of the codes leads to significantly better thresholds when compared to corresponding LDPC block codes.