Algebraic Fast-Decodable Relay Codes for Distributed Communications

TL;DR

This paper introduces algebraic lattice code constructions for NAF MIMO channels that enable fast decoding by leveraging algebraic structures like quaternion division algebras, with further complexity reduction through code shortening.

Contribution

It presents novel algebraic lattice code designs for NAF MIMO channels that significantly reduce decoding complexity using algebraic structures and code shortening techniques.

Findings

Codes achieve reduced decoding complexity

Algebraic structures facilitate fast decoding

Code shortening further decreases complexity

Abstract

In this paper, fast-decodable lattice code constructions are designed for the nonorthogonal amplify-and-forward (NAF) multiple-input multiple-output (MIMO) channel. The constructions are based on different types of algebraic structures, e.g. quaternion division algebras. When satisfying certain properties, these algebras provide us with codes whose structure naturally reduces the decoding complexity. The complexity can be further reduced by shortening the block length, i.e., by considering rectangular codes called less than minimum delay (LMD) codes.