Minimizing the Complexity of Fast Sphere Decoding of STBCs

TL;DR

This paper introduces a quadratic form called the Hurwitz-Radon QF to analyze and minimize the complexity of fast sphere decoding of linear space-time block codes, independent of channel realization.

Contribution

It provides a new QF-based interpretation of FSD complexity and an algorithm to optimize weight matrix ordering for reduced decoding complexity.

Findings

FSD complexity depends only on code structure, not channel realization.

A single matrix captures the FSD complexity of a code.

The framework unifies known low-complexity code classes.

Abstract

Decoding of linear space-time block codes (STBCs) with sphere-decoding (SD) is well known. A fast-version of the SD known as fast sphere decoding (FSD) has been recently studied by Biglieri, Hong and Viterbo. Viewing a linear STBC as a vector space spanned by its defining weight matrices over the real number field, we define a quadratic form (QF), called the Hurwitz-Radon QF (HRQF), on this vector space and give a QF interpretation of the FSD complexity of a linear STBC. It is shown that the FSD complexity is only a function of the weight matrices defining the code and their ordering, and not of the channel realization (even though the equivalent channel when SD is used depends on the channel realization) or the number of receive antennas. It is also shown that the FSD complexity is completely captured into a single matrix obtained from the HRQF. Moreover, for a given set of weight matrices, an algorithm to obtain a best ordering of them leading to the least FSD complexity is presented. The well known classes of low FSD complexity codes (multi-group decodable codes, fast decodable codes and fast group decodable codes) are presented in the framework of HRQF.