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Flexible Low-Density Parity-Check Codes: Rate, Length, and Complexity

Author:
Moritz Beermann
Editor:
Peter Vary
Type:
Dissertation
Series:
Aachener Beiträge zu Digitalen Nachrichtensystemen (ABDN)
Number:
42
School:
IND, RWTH Aachen
Publisher:
Verlag Mainz in Aachen
Location:
Aachen
Date:
2016
ISBN:
978-3-95886-083-4
Language:
English

Abstract

Since the inception of information theory by Shannon in 1948, a vast amount of research has been conducted concerning error correcting codes for communication over noisy channels. Low-Density Parity-Check (LDPC) codes represent one important class of such channel codes that are capable of closely approaching the fundamental capacity limits for sufficiently large code lengths. One observable trend in the conventional design process is that the closer a code performs within the given theoretical limits, the more specifically it needs to be tailored towards the exact considered transmission setup. This process, however, does not account for the growing heterogeneity and varying requirements of future (mobile) communication systems.

 

Facilitating this heterogeneity, an alternative design strategy is developed in this thesis that is not restricted to a single transmission scenario but instead enables a unified design of highly flexible LDPC codes. As foundation, the traditional design process of LDPC codes is reviewed, which consists of two disciplines: the asymptotic analysis that predicts the average performance of a code ensemble and the actual construction of a specific code comprising finite length effects that ultimately determine the code’s error correction capabilities.

 

The main part of this thesis introduces and analyzes novel concepts for the design of multi-rate LDPC codes and multi-length LDPC codes, denoting codes that are based on a single mother code but are capable of achieving several code rates or lengths, respectively. This design enables efficient transmission and reconstruction of data at several channel qualities, delay requirements, and data rates, while reducing the complexity compared to current state-of-the-art concepts to a large extent. To achieve multi-rate capabilities, a novel joint consideration of the well-known information shortening and parity puncturing techniques is introduced, including analysis and optimization of both asymptotic ensemble performance as well as finite length effects. Furthermore, two new concepts are introduced and evaluated to add multi-length features into LDPC code design to further enhance flexibility: multi-length LDPC codes by concurrent shortening and puncturing and multi-length quasi-cyclic (QC) LDPC codes by jointly optimized lifting matrix construction. Both of these concepts are shown to be directly compatible with the proposed multi-rate design, resulting in combined multi-rate-and-multi-length LDPC codes that surpass the flexibility of all previously known LDPC code designs.

 

Advances in terms of flexible decoding algorithms and their implementations are presented to also meet the demands of the growing variety of heterogeneous devices with different computational capabilities and their manifold requirements in terms of error correction performance, computational complexity, and convergence speed. Two novel decoder schedules are introduced that are motivated by these kinds of flexibility requirements. Finally, the first fully generic non-binary LDPC decoder implementation on a graphics processing unit (GPU) is presented, that is capable of achieving high speedups without any algorithmic approximations.