Covariance Evolution for Spatially "Mt. Fuji" Coupled LDPC Codes

TL;DR

This paper extends covariance evolution analysis to a modified 'Mt. Fuji' coupled LDPC ensemble, providing insights into its decoding error probability in the waterfall region over the BEC.

Contribution

It introduces a modified covariance evolution method to analyze the waterfall region error probability of the 'Mt. Fuji' coupled LDPC codes.

Findings

The analysis confirms the desirable properties of the 'Mt. Fuji' ensemble.

Theoretical decoding error probability in the waterfall region is derived.

The method enhances understanding of error behavior in spatially coupled LDPC codes.

Abstract

A spatially "Mt. Fuji" coupled low-density parity check (LDPC) ensemble is a modified version of the original spatially coupled (SC) LDPC ensemble. Its desirable properties are first observed in experimentally. The decoding error probability in the error floor region over the binary erasure channel (BEC) is theoretically analyzed later. In this paper, as the last piece of the theoretical analysis over the BEC, we analyze the decoding error probability in the waterfall region by modifying the covariance evolution which has been used to analyze the original SC-LDPC ensemble.