Iterated Space-Time Code Constructions from Cyclic Algebras

TL;DR

This paper introduces a method to construct full-rate, high-dimensional space-time codes from cyclic algebra-based codes, analyzing their diversity and decoding complexity, especially for 2 and 3-dimensional cases.

Contribution

It presents a novel iterated code construction technique from cyclic algebras and provides conditions for full-diversity, with detailed analysis for MIDO and triple-input cases.

Findings

Derived conditions for full-diversity of the codes

Analyzed maximum likelihood decoding complexity

Developed new methods for obtaining division algebras

Abstract

We propose a full-rate iterated space-time code construction, to design 2n-dimensional codes from n-dimensional cyclic algebra based codes. We give a condition to determine whether the resulting codes satisfy the full-diversity property, and study their maximum likelihood decoding complexity with respect to sphere decoding. Particular emphasis is given to the cases n = 2, sometimes referred to as MIDO (multiple input double output) codes, and n = 3. In the process, we derive an interesting way of obtaining division algebras, and study their center and maximal subfield.