Algebraic Distributed Differential Space-Time Codes with Low Decoding Complexity

TL;DR

This paper introduces a new class of algebraic distributed differential space-time codes using extended Clifford algebras, enabling low-complexity decoding and improved performance in relay networks and multiple antenna systems.

Contribution

It extends existing differential space-time coding frameworks to scaled unitary matrices and proposes a novel algebraic code construction with full diversity and low decoding complexity.

Findings

Codes outperform cyclic and circulant codes in simulations.

Applicable to relay networks with power of two relays.

Achieves full cooperative diversity with low complexity decoding.

Abstract

The differential encoding/decoding setup introduced by Kiran et al, Oggier-Hassibi and Jing-Jafarkhani for wireless relay networks that use codebooks consisting of unitary matrices is extended to allow codebooks consisting of scaled unitary matrices. For such codebooks to be usable in the Jing-Hassibi protocol for cooperative diversity, the conditions involving the relay matrices and the codebook that need to be satisfied are identified. Using the algebraic framework of extended Clifford algebras, a new class of Distributed Differential Space-Time Codes satisfying these conditions for power of two number of relays and also achieving full cooperative diversity with a low complexity sub-optimal receiver is proposed. Simulation results indicate that the proposed codes outperform both the cyclic codes as well as the circulant codes. Furthermore, these codes can also be applied as Differential Space-Time codes for non-coherent communication in classical point to point multiple antenna systems.