Computing the minimum distance of nonbinary LDPC codes using block Korkin-Zolotarev method

TL;DR

This paper introduces a new algorithm based on the BKZ lattice reduction method to efficiently compute the minimum distance of nonbinary LDPC codes, especially effective for large code lengths and sparse lattices.

Contribution

The paper presents a novel BKZ-based algorithm for measuring code distance in nonbinary LDPC codes, including an upper bound proof and potential for probabilistic enhancements.

Findings

Linear decrease in runtime with number of threads

Effective for codes with length several thousand

Suitable for sparse LDPC lattices

Abstract

In article present measure code distance algorithm of binary and ternary linear block code using block Korkin-Zolotarev (BKZ). Proved the upper bound on scaling constant for measure code distance of non-systematic linear block code using BKZ-method for different value of the block size. Introduced method show linear decrease of runtime from number of threads and work especially good under not dense lattices of LDPC-code. These properties allow use this algorithm to measure the minimal distance of code with length several thousand. The algorithm can further improve by transform into probabilistic algorithm using lattice enumerating pruning techniques