Minimum Distances of the QC-LDPC Codes in IEEE 802 Communication Standards

TL;DR

This paper analyzes the minimum distances of QC-LDPC codes in IEEE 802 standards, providing bounds and actual minimum distances for various code configurations, addressing computational challenges in the process.

Contribution

It applies theoretical bounds and computational methods to determine minimum distances of QC-LDPC codes in IEEE 802 standards, enhancing understanding of their error-correcting capabilities.

Findings

Bounds on minimum distances independent of block length

Minimum distances achieved for specific parity check matrices

Solutions to computational challenges in minimum distance calculation

Abstract

This work applies earlier results on Quasi-Cyclic (QC) LDPC codes to the codes specified in six separate IEEE 802 standards, specifying wireless communications from 54 MHz to 60 GHz. First, we examine the weight matrices specified to upper bound the codes' minimum distance independent of block length. Next, we search for the minimum distance achieved for the parity check matrices selected at each block length. Finally, solutions to the computational challenges encountered are addressed.