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IEEE Symposium on Computers and Communications (ISCC)

A survey on decoding schedules of LDPC convolutional codes and associated hardware architectures

Hayfa Ben Thameur, Bertrand Le Gal, Nadia Khouja, Fethi Tlili, Christophe Jégo

Published Jul 1, 2017• 8 citations
Publisher

Abstract

Low-density parity-check convolutional codes (LDPC-CC) have interesting error correction features. They have a great potential to become a key error-correcting codes for enhancing reliability of modern digital communication systems, optical systems and storage devices. On the implementation side, however, the design of low-cost low-power and high-throughput LDPC-CC decoders remains challenging. This survey paper provides an overview of the state-of-the-art of different algorithmic optimizations proposed to ease and improve the LDPC-CC decoder implementations. To this end, a summary of the available decoding scheduling approaches is provided. Besides, a complexity analysis, performance comparison and an architectural analysis of LDPC-CC decoders based on different scheduling techniques is detailed.

DOI
10.1109/iscc.2017.8024640

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Low-density parity-check convolutional codes (LDPC-CC) have interesting error correction features. They have a great potential to become a key error-correcting codes for enhancing reliability of modern digital communication systems, optical systems and storage devices. On the implementation side, however, the design of low-cost low-power and high-throughput LDPC-CC decoders remains challenging. This survey paper provides an overview of the state-of-the-art of different algorithmic optimizations proposed to ease and improve the LDPC-CC decoder implementations. To this end, a summary of the available decoding scheduling approaches is provided. Besides, a complexity analysis, performance comparison and an architectural analysis of LDPC-CC decoders based on different scheduling techniques is detailed.
Non-binary low-density parity-check (NB-LDPC) codes show higher error-correcting performance than binary low-density parity-check (LDPC) codes when the codeword length is moderate and/or the channel has bursts of errors. The need for high-speed decoders for future digital communications led to the investigation of optimized NB-LDPC decoding algorithms and efficient implementations that target high throughput and low energy consumption levels. We carried out a comprehensive survey of existing NB-LDPC decoding hardware that targets the optimization of these parameters. Even though existing NB-LDPC decoders are optimized with respect to computational complexity and memory requirements, they still lag behind their binary counterparts in terms of throughput, power and area optimization. This study contributes to an overall understanding of the state-of-the-art on application-specific integrated-circuit (ASIC), field-programmable gate array (FPGA) and graphics processing units (GPU) based systems, and highlights the current challenges that still have to be overcome on the path to more efficient NB-LDPC decoder architectures.
Low-density parity-check (LDPC) codes had a renaissance when they were rediscovered in the 1990’s. Since then LDPC codes have been an important part of the field of error-correcting codes, and have been shown to be able to approach the Shannon capacity, the limit at which we can reliably transmit information over noisy channels. Following this, many modern communications standards have adopted LDPC codes. Error-correction is equally important in protecting data from corruption on a hard-drive as it is in deep-space communications. It is most commonly used for example for reliable wireless transmission of data to mobile devices. For practical purposes, both encoding and decoding need to be of low complexity to achieve high throughput and low power consumption. This thesis provides a literature review of the current state-of-the-art in encoding and decoding of LDPC codes. Message- passing decoders are still capable of achieving the best error-correcting performance, while more recently considered bit-flipping decoders are providing a low-complexity alternative, albeit with some loss in error-correcting performance. An implementation of a low-complexity stochastic bit-flipping decoder is also presented. It is implemented for Graphics Processing Units (GPUs) in a parallel fashion, providing a peak throughput of 1.2 Gb/s, which is significantly higher than previous decoder implementations on GPUs. The error-correcting performance of a range of decoders has also been tested, showing that the stochastic bit-flipping decoder provides relatively good error-correcting performance with low complexity. Finally, a brief comparison of encoding complexities for two code ensembles is also presented.
LDPC convolutional codes (LDPC-CC) are a family of error-correcting codes (ECC) used in digital communication systems like the IEEE 1901 standard. High throughput and low complexity hardware architectures were designed for real time systems. In this article we demonstrate that an efficient selection of the message passing (MP) algorithm for LDPC-CC decoding improves the architecture features of related works. In fact, considering the LDPC-CC decoders proposed for the IEEE 1901 standard, we show that an appropriate Min-Sum approximation selection can significantly improve the error correction performance by 0.1 to 0.2 dB in terms of Bit Error Ratio. It can also reduce the hardware complexity by 10% to 20% with no impact on the Bit Error Ratio performance.
The Low-Density Parity-Check codes are among the most powerful forward error correcting codes, since they enable to get as close as a fraction of a dB from the Shannon limit.This astonishing performance combined with their relatively simple decoding algorithmmake these codes very attractive for the next digital transmission system generations. Itis already the case for the next digital satellite broadcasting standard (DVB-S2), where an irregular LDPC code has been chosen to protect the downlink information. In this thesis, we focused our research on the iterative decoding algorithms and their hardware implementations. We proposed first a suboptimal algorithm named the λ-min algorithm. It reduces significantly the complexity of the decoder without any significant performance loss, as compared to the belief propagation (BP) algorithm. Then we studied and designed a generic architecture of an LDPC decoder, which has been implemented on a FPGA based platform. This hardware decoder enables to accelerate the simulations more than 500 times as compared to software simulations. Moreover, based on an all-tunable design, our decoder features many facilities: It is possible to configure it for a very wide code family, so that the research for good codes is processed faster ; thanks to the genericity of the processing components, it is also possible to optimize the internal coding format, and even to compare various decoding algorithms and various processing schedules. Finally, our experience in the area of LDPC decoders led us to propose a formal framework for analysing the architectures of LDPC decoders. This framework encompassesboth the datapath (parallelism, node processors architectures) and the control mode associated to the several decoding schedules. Thus within this framework, a classification of the different state-of-the-art LDPC decoders is proposed. Moreover, some synthesis of efficient and unpublished architectures have been also proposed.
The ADMM based linear programming (LP) technique shows interesting error correction performance when decoding binary LDPC block codes. Nonetheless, it's applicability to decode LDPC convolutional codes (LDPC-CC) has not been yet investigated. In this paper, a first flooding based formulation of the ADMM-LP for decoding LDPC-CCs is described. In addition, reduced complexity decoding schedules to lessen the storage requirements and improve the convergence speed of an ADMM-LP based LDPC-CC decoder without significant loss in error correction performances are proposed and assessed from an algorithmic and computational/memory complexity perspectives.
5G technology new radios (5G NR) require high-speed decoders that operate on highly irregular low-density parity-check (LDPC) codes.LDPC decoders have gained significant attention due to their excellent error correction performance.This study evaluates on different algorithms and scheduling techniques used for LDPC decoders.The analysis highlights that Min-Sum-based approaches can reduce the computational complexity compared to the basic sum-product algorithm, while the normalized and extended Min-Sum algorithms provide a better trade-off owing to their accurate value assumptions.Furthermore, different scheduling methods are implied for MS to improve speed and reduce latency.This study provides a comparative analysis of the algorithms and architectures that yield high throughputs without compromising performance efficiency.The LNMS algorithm with a data-level rescheduling technique resolves data dependency issues.This resolves the complexity of CN and VN and improves the throughput, making it suitable for 5G NR applications.The decoded throughput achieved with this scheduling is 7.0 Gbps.This throughput is achieved by maintaining the standard parameters and worst case parameters, such as four/eight iterations, BG1, and a code rate of 0.8/0.5.The evaluated architectures are implemented on Field Programmable Gate Array (FPGA) devices.This study aids in selecting the optimal architecture and scheduling techniques for LDPC decoders by considering various performance standards to deploy wireless networks in 5G and beyond.