Fast-Group-Decodable STBCs via Codes over GF(4)

TL;DR

This paper introduces a novel method for constructing low decoding complexity space-time block codes (STBCs) using codes over GF(4), simplifying the orthogonality condition and unifying known codes with new, efficient designs.

Contribution

It presents a new approach to design low complexity STBCs via GF(4) codes, enabling easier verification of orthogonality and generating both known and novel codes.

Findings

Most known low complexity STBCs can be derived using this GF(4) approach.

New codes with minimal decoding complexity are constructed for specific rate ranges.

The orthogonality condition is simplified by transferring the problem to the GF(4) domain.

Abstract

In this paper we construct low decoding complexity STBCs by using the Pauli matrices as linear dispersion matrices. In this case the Hurwitz-Radon orthogonality condition is shown to be easily checked by transferring the problem to $\mathbb{F}_4$ domain. The problem of constructing low decoding complexity STBCs is shown to be equivalent to finding certain codes over $\mathbb{F}_4$. It is shown that almost all known low complexity STBCs can be obtained by this approach. New codes are given that have the least known decoding complexity in particular ranges of rate.