Low complexity soft demapping for non-binary LDPC codes

Alain Mourad,Marco Luise,Ottavio Picchi,Ismael Gutierrez

doi:10.1186/1687-1499-2012-55

Abstract

This article focuses on non-binary wireless transmission, where "non-binary" refers to the use of non-binary Low Density Parity Check (LDPC) codes for Forward Error Correction. The complexity of the non-binary soft demapper is addressed in particular when one non-binary Galois Field (GF) symbol spreads across multiple Quadrature Amplitude Modulation (QAM) symbols and Space-Time Block Code (STBC) codewords. A strategy is devised to guarantee an efficient mapping at the transmitter, together with an algorithm at the receiver for low complexity soft Maximum Likelihood demapping. The proposed solution targets a trade-off between performance and complexity, and removes any restriction on the setting of the GF order, QAM constellation order, and STBC scheme. This makes the non-binary LDPC codes even more appealing for potential use in practical wireless communication systems.

Highlights

Non-binary channel codes (i.e., defined over high-order Galois Field (GF) q > 2) have been researched in the literature to achieve higher error protection than conventional binary codes for transmission over different noisy channels [1,2,3]
This article tackles the challenging complexity of the non-binary soft demapper when the GF symbol spreads across multiple Quadrature Amplitude Modulation (QAM) symbols and Space-Time Block Code (STBC) codewords
In this article, we have addressed the particular complexity challenge of the soft Maximum Likelihood (ML) demapping faced with non-binary Low Density Parity Check (LDPC) codes when one GF(q) symbol spreads across multiple QAM symbols and STBC codewords

Summary

Introduction

Non-binary channel codes (i.e., defined over high-order Galois Field (GF) q > 2) have been researched in the literature to achieve higher error protection than conventional binary codes for transmission over different noisy channels [1,2,3]. The proposed non-binary LDPC codes were shown to outperform their binary counterparts, e.g., binary LDPC and (duo-) binary Turbo Codes, with higher gains for higher constellation orders and higher coding rates [5]. These non-binary codes were shown to boost the system spectral efficiency when combined with highorder Quadrature Amplitude Modulation (QAM) constellations and MIMO spatial multiplexing [6]. This boosting effect comes from the inherently higher capacity of the single-input single-output (SISO) equivalent

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Conclusion