Space-Time Codes Based on Rank-Metric Codes and Their Decoding

TL;DR

This paper introduces a novel class of space-time block codes based on finite-field rank-metric codes, achieving maximum diversity and offering a polynomial-complexity decoding algorithm suitable for large systems.

Contribution

The paper presents a new construction of space-time codes using rank-metric codes and a rank-preserving mapping, along with an efficient decoding method leveraging algebraic structure.

Findings

Codes achieve maximum diversity order

Decoding algorithm has polynomial complexity

Improved performance over some existing constructions

Abstract

We propose a new class of space-time block codes based on finite-field rank-metric codes in combination with a rank-metric-preserving mapping to the set of Eisenstein integers. It is shown that these codes achieve maximum diversity order and improve upon certain existing constructions. Moreover, we present a new decoding algorithm for these codes which utilizes the algebraic structure of the underlying finite-field rank-metric codes and employs lattice-reduction-aided equalization. This decoder does not achieve the same performance as the classical maximum-likelihood decoding methods, but has polynomial complexity in the matrix dimension, making it usable for large field sizes and numbers of antennas.