Efficient decoding algorithm using triangularity of $\mbf{R}$ matrix of QR-decomposition

TL;DR

This paper introduces 'divided decoder', an efficient decoding algorithm leveraging the triangular structure of the R matrix in QR-decomposition, offering flexible performance and complexity trade-offs for various decoding methods.

Contribution

The paper proposes a novel 'divided decoder' algorithm that enhances decoding flexibility by combining multiple search algorithms using QR-decomposition, with theoretical analysis and simulation validation.

Findings

Provides diversity order and error rate bounds for typical models

Demonstrates flexibility in performance and complexity trade-offs

Simulation results confirm theoretical predictions

Abstract

An efficient decoding algorithm named `divided decoder' is proposed in this paper. Divided decoding can be combined with any decoder using QR-decomposition and offers different pairs of performance and complexity. Divided decoding provides various combinations of two or more different searching algorithms. Hence it makes flexibility in error rate and complexity for the algorithms using it. We calculate diversity orders and upper bounds of error rates for typical models when these models are solved by divided decodings with sphere decoder, and discuss about the effects of divided decoding on complexity. Simulation results of divided decodings combined with a sphere decoder according to different splitting indices correspond to the theoretical analysis.