A Cutting Plane Method based on Redundant Rows for Improving Fractional Distance

TL;DR

This paper introduces a cutting plane method utilizing redundant rows to enhance the fractional distance of binary parity check matrices, thereby improving decoding performance in error correction.

Contribution

It presents a novel approach using redundant rows and a greedy algorithm to effectively increase the fractional distance of parity check matrices.

Findings

Significant increase in fractional distance achieved

Efficient implementation of the proposed algorithm

Potential improvements in decoding accuracy

Abstract

In this paper, an idea of the cutting plane method is employed to improve the fractional distance of a given binary parity check matrix. The fractional distance is the minimum weight (with respect to l1-distance) of vertices of the fundamental polytope. The cutting polytope is defined based on redundant rows of the parity check matrix and it plays a key role to eliminate unnecessary fractional vertices in the fundamental polytope. We propose a greedy algorithm and its efficient implementation for improving the fractional distance based on the cutting plane method.