Decoding Complexity of Irregular LDGM-LDPC Codes Over the BISOM Channels

TL;DR

This paper analyzes irregular LDGM-LDPC codes, demonstrating they can approach channel capacity with bounded complexity and providing bounds on their check-node degrees, applicable to various decoders.

Contribution

It introduces a lower bound on check-node degrees for irregular LDGM-LDPC codes and explores their capacity-approaching performance with complexity constraints.

Findings

Codes achieve rates close to channel capacity

Lower bound on check-node degree established

Stability condition for decoding over BEC derived

Abstract

An irregular LDGM-LDPC code is studied as a sub-code of an LDPC code with some randomly \emph{punctured} output-bits. It is shown that the LDGM-LDPC codes achieve rates arbitrarily close to the channel-capacity of the binary-input symmetric-output memoryless (BISOM) channel with bounded \emph{complexity}. The measure of complexity is the average-degree (per information-bit) of the check-nodes for the factor-graph of the code. A lower-bound on the average degree of the check-nodes of the irregular LDGM-LDPC codes is obtained. The bound does not depend on the decoder used at the receiver. The stability condition for decoding the irregular LDGM-LDPC codes over the binary-erasure channel (BEC) under iterative-decoding with message-passing is described.