Single-Symbol Maximum Likelihood Decodable Linear STBCs

TL;DR

This paper characterizes all linear space-time block codes that enable single-symbol maximum likelihood decoding over quasi-static fading channels, expanding beyond known designs like OD and CIOD.

Contribution

It identifies and classifies all linear STBCs allowing single-symbol ML decoding, including those not previously known, and introduces the class of full-diversity SDDs.

Findings

SDD includes OD and CIOD as subclasses

Full-rank SDDs offer full diversity

Complete characterization of single-symbol decodable linear STBCs

Abstract

Space-Time block codes (STBC) from Orthogonal Designs (OD) and Co-ordinate Interleaved Orthogonal Designs (CIOD) have been attracting wider attention due to their amenability for fast (single-symbol) ML decoding, and full-rate with full-rank over quasi-static fading channels. However, these codes are instances of single-symbol decodable codes and it is natural to ask, if there exist codes other than STBCs form ODs and CIODs that allow single-symbol coding? In this paper, the above question is answered in the affirmative by characterizing all linear STBCs, that allow single-symbol ML decoding (not necessarily full-diversity) over quasi-static fading channels-calling them single-symbol decodable designs (SDD). The class SDD includes ODs and CIODs as proper subclasses. Further, among the SDD, a class of those that offer full-diversity, called Full-rank SDD (FSDD) are characterized and classified.