Generalized Distributive Law for ML Decoding of Space-Time Block Codes

TL;DR

This paper introduces a new GDL-based framework for decoding space-time block codes, offering reduced complexity over traditional methods and encompassing existing decodable code classes.

Contribution

It proposes a generalized GDL decoding approach for STBCs, providing conditions for fast GDL decodability and demonstrating complexity reductions over conventional CML decoding.

Findings

GDL decoding complexity is strictly less than CML for all STBCs.

Multigroup and conditionally multigroup decodable codes are fast GDL decodable.

GDL offers about 12 times reduction in complexity for certain codes.

Abstract

The problem of designing good Space-Time Block Codes (STBCs) with low maximum-likelihood (ML) decoding complexity has gathered much attention in the literature. All the known low ML decoding complexity techniques utilize the same approach of exploiting either the multigroup decodable or the fast-decodable (conditionally multigroup decodable) structure of a code. We refer to this well known technique of decoding STBCs as Conditional ML (CML) decoding. In this paper we introduce a new framework to construct ML decoders for STBCs based on the Generalized Distributive Law (GDL) and the Factor-graph based Sum-Product Algorithm. We say that an STBC is fast GDL decodable if the order of GDL decoding complexity of the code is strictly less than M^l, where l is the number of independent symbols in the STBC, and M is the constellation size. We give sufficient conditions for an STBC to admit fast GDL decoding, and show that both multigroup and conditionally multigroup decodable codes are fast GDL decodable. For any STBC, whether fast GDL decodable or not, we show that the GDL decoding complexity is strictly less than the CML decoding complexity. For instance, for any STBC obtained from Cyclic Division Algebras which is not multigroup or conditionally multigroup decodable, the GDL decoder provides about 12 times reduction in complexity compared to the CML decoder. Similarly, for the Golden code, which is conditionally multigroup decodable, the GDL decoder is only half as complex as the CML decoder.