LP-decodable multipermutation codes

TL;DR

This paper introduces a novel class of LP-decodable multipermutation codes, characterizes their convex hull, and develops two LP decoding algorithms for memoryless channels and Chebyshev distance minimization.

Contribution

It presents a new construction of multipermutation codes using multipermutation matrices and provides LP decoding algorithms based on convex hull characterization.

Findings

Successful formulation of LP decoding problem for multipermutation codes

Development of an LP algorithm for Chebyshev distance minimization

Numerical example demonstrating the effectiveness of the proposed algorithms

Abstract

In this paper, we introduce a new way of constructing and decoding multipermutation codes. Multipermutations are permutations of a multiset that may consist of duplicate entries. We first introduce a new class of matrices called multipermutation matrices. We characterize the convex hull of multipermutation matrices. Based on this characterization, we propose a new class of codes that we term LP-decodable multipermutation codes. Then, we derive two LP decoding algorithms. We first formulate an LP decoding problem for memoryless channels. We then derive an LP algorithm that minimizes the Chebyshev distance. Finally, we show a numerical example of our algorithm.