On Achievable Rates and Complexity of LDPC Codes for Parallel Channels: Information-Theoretic Bounds and Applications

TL;DR

This paper derives bounds on the achievable rates and decoding complexity of LDPC codes over parallel channels, providing insights into their performance and applications, especially for punctured LDPC codes.

Contribution

It introduces new bounds on LDPC code rates and complexity in parallel channels, connecting theoretical results with practical code design.

Findings

Bounds on achievable rates for LDPC codes over parallel channels

Decoding complexity limits established for these codes

Application of bounds to punctured LDPC codes

Abstract

The paper presents bounds on the achievable rates and the decoding complexity of low-density parity-check (LDPC) codes. It is assumed that the communication of these codes takes place over statistically independent parallel channels where these channels are memoryless, binary-input and output-symmetric (MBIOS). The bounds are applied to punctured LDPC codes. A diagram concludes our discussion by showing interconnections between the theorems in this paper and some previously reported results.