Comparison of Polar Decoders with Existing Low-Density Parity-Check and Turbo Decoders

Polar codes are a recently proposed family of provably capacity-achieving error-correction codes that received a lot of attention. While their theoretical properties render them interesting, their practicality compared to other types of codes has not been thoroughly studied. Towards this end, in this paper, we perform a comparison of polar decoders against LDPC and Turbo decoders that are used in existing communications standards. More specifically, we compare both the error-correction performance and the hardware efficiency of the corresponding hardware implementations. This comparison enables us to identify applications where polar codes are superior to existing error-correction coding solutions as well as to determine the most promising research direction in terms of the hardware implementation of polar decoders.Comment: Fixes small mistakes from the paper to appear in the proceedings of IEEE WCNC 2017. Results were presented in the "Polar Coding in Wireless Communications: Theory and Implementation" Worksho

Concatenated Turbo/LDPC codes for deep space communications: performance and implementation

Deep space communications require error correction codes able to reach extremely low bit-error-rates, possibly with a steep waterfall region and without error floor. Several schemes have been proposed in the literature to achieve these goals. Most of them rely on the concatenation of different codes that leads to high hardware implementation complexity and poor resource sharing. This work proposes a scheme based on the concatenation of non-custom LDPC and turbo codes that achieves excellent error correction performance. Moreover, since both LDPC and turbo codes can be decoded with the BCJR algorithm, our preliminary results show that an efficient hardware architecture with high resource reuse can be designe

Deriving Good LDPC Convolutional Codes from LDPC Block Codes

Low-density parity-check (LDPC) convolutional codes are capable of achieving excellent performance with low encoding and decoding complexity. In this paper we discuss several graph-cover-based methods for deriving families of time-invariant and time-varying LDPC convolutional codes from LDPC block codes and show how earlier proposed LDPC convolutional code constructions can be presented within this framework. Some of the constructed convolutional codes significantly outperform the underlying LDPC block codes. We investigate some possible reasons for this "convolutional gain," and we also discuss the --- mostly moderate --- decoder cost increase that is incurred by going from LDPC block to LDPC convolutional codes.Comment: Submitted to IEEE Transactions on Information Theory, April 2010; revised August 2010, revised November 2010 (essentially final version). (Besides many small changes, the first and second revised versions contain corrected entries in Tables I and II.

An Iteratively Decodable Tensor Product Code with Application to Data Storage

The error pattern correcting code (EPCC) can be constructed to provide a syndrome decoding table targeting the dominant error events of an inter-symbol interference channel at the output of the Viterbi detector. For the size of the syndrome table to be manageable and the list of possible error events to be reasonable in size, the codeword length of EPCC needs to be short enough. However, the rate of such a short length code will be too low for hard drive applications. To accommodate the required large redundancy, it is possible to record only a highly compressed function of the parity bits of EPCC's tensor product with a symbol correcting code. In this paper, we show that the proposed tensor error-pattern correcting code (T-EPCC) is linear time encodable and also devise a low-complexity soft iterative decoding algorithm for EPCC's tensor product with q-ary LDPC (T-EPCC-qLDPC). Simulation results show that T-EPCC-qLDPC achieves almost similar performance to single-level qLDPC with a 1/2 KB sector at 50% reduction in decoding complexity. Moreover, 1 KB T-EPCC-qLDPC surpasses the performance of 1/2 KB single-level qLDPC at the same decoder complexity.Comment: Hakim Alhussien, Jaekyun Moon, "An Iteratively Decodable Tensor Product Code with Application to Data Storage

Hardware Implementations of CCSDS Deep Space LDPC Codes for a Satellite Transponder

Error-correction coding is a technique that adds mathematical structure to a message, allowing corruptions to be detected and corrected when the message is received. This is especially important for deep space satellite communications, since the long distances and low signal power levels often cause message corruption. A very strong type of error-correction coding known as LDPC codes was recently standardized for use with space communications. This project implements the encoding and decoding algorithms required for a small satellite radio to be able to use these LDPC codes. Several decoder architectures are implemented and compared by their performance, speed, and complexity. Using these LDPC decoders requires knowledge of the received signal and noise levels, so an appropriate algorithm for estimating these parameters is developed and implemented. The LDPC encoder is implemented using a flexible architecture that allows the entire standardized family of ten LDPC codes to be encoded using the same hardware

A Flexible LDPC/Turbo Decoder Architecture

Low-density parity-check (LDPC) codes and convolutional Turbo codes are two of the most powerful error correcting codes that are widely used in modern communication systems. In a multi-mode baseband receiver, both LDPC and Turbo decoders may be required. However, the different decoding approaches for LDPC and Turbo codes usually lead to different hardware architectures. In this paper we propose a unified message passing algorithm for LDPC and Turbo codes and introduce a flexible soft-input soft-output (SISO) module to handle LDPC/Turbo decoding. We employ the trellis-based maximum a posteriori (MAP) algorithm as a bridge between LDPC and Turbo codes decoding. We view the LDPC code as a concatenation of n super-codes where each super-code has a simpler trellis structure so that the MAP algorithm can be easily applied to it. We propose a flexible functional unit (FFU) for MAP processing of LDPC and Turbo codes with a low hardware overhead (about 15% area and timing overhead). Based on the FFU, we propose an area-efficient flexible SISO decoder architecture to support LDPC/Turbo codes decoding. Multiple such SISO modules can be embedded into a parallel decoder for higher decoding throughput. As a case study, a flexible LDPC/Turbo decoder has been synthesized on a TSMC 90 nm CMOS technology with a core area of 3.2 mm2. The decoder can support IEEE 802.16e LDPC codes, IEEE 802.11n LDPC codes, and 3GPP LTE Turbo codes. Running at 500 MHz clock frequency, the decoder can sustain up to 600 Mbps LDPC decoding or 450 Mbps Turbo decoding.NokiaNokia Siemens Networks (NSN)XilinxTexas InstrumentsNational Science Foundatio

UNIFIED DECODER ARCHITECTURE FOR LDPC/TURBO CODES

Low-density parity-check (LDPC) codes on par with convolutional turbo codes (CTC) are two of the most powerful error correction codes known to perform very close to the Shannon limit. However, their different code structures usually lead to different hardware implementations. In this paper, we propose a unified decoder architecture that is capable of decoding both LDPC and turbo codes with a limited hardware overhead. We employ maximum a posteriori (MAP) algorithm as a bridge between LDPC and turbo codes. We represent LDPC codes as parallel concatenated single parity check (PCSPC) codes and propose a group sub-trellis (GST) decoding algorithm for the efficient decoding of PCSPC codes. This algorithm achieves about 2X improvement in the convergence speed and is more numerically robust than the classical ”tanh” algorithm. What is more interesting is that we can generalize a unified trellis decoding algorithm for LDPC and turbo codes based on their trellis structures. We propose a reconfigurable computation kernel for log-MAP decoding of LDPC and turbo codes at a cost of ∼15% hardware overhead. Small lookup tables (LUTs) with 9 entries of 2-bit data are designed to implement the log-MAP algorithm. Fixed point (6:2) simulation results show that there is negligible or nearly no performance loss by using this LUT approximation compared to the ideal case. The proposed architecture results in scalable and flexible datapath units enabling parallel decoding of LDPC/turbo codes.NokiaNational Science Foundatio

A Massively Parallel Implementation of QC-LDPC Decoder on GPU

The graphics processor unit (GPU) is able to provide a low-cost and flexible software-based multi-core architecture for high performance computing. However, it is still very challenging to efficiently map the real-world applications to GPU and fully utilize the computational power of GPU. As a case study, we present a GPU-based implementation of a real-world digital signal processing (DSP) application: low-density parity-check (LDPC) decoder. The paper shows the efforts we made to map the algorithm onto the massively parallel architecture of GPU and fully utilize GPU’s computational resources to significantly boost the performance. Moreover, several efficient data structures have been proposed to reduce the memory access latency and the memory bandwidth requirement. Experimental results show that the proposed GPU-based LDPC decoding accelerator can take advantage of the multi-core computational power provided by GPU and achieve high throughput up to 100.3Mbps.Renesas MobileTexas InstrumentsXilinxNational Science Foundatio

A survey of FPGA-based LDPC decoders

Low-Density Parity Check (LDPC) error correction decoders have become popular in communications systems, as a benefit of their strong error correction performance and their suitability to parallel hardware implementation. A great deal of research effort has been invested into LDPC decoder designs that exploit the flexibility, the high processing speed and the parallelism of Field-Programmable Gate Array (FPGA) devices. FPGAs are ideal for design prototyping and for the manufacturing of small-production-run devices, where their in-system programmability makes them far more cost-effective than Application-Specific Integrated Circuits (ASICs). However, the FPGA-based LDPC decoder designs published in the open literature vary greatly in terms of design choices and performance criteria, making them a challenge to compare. This paper explores the key factors involved in FPGA-based LDPC decoder design and presents an extensive review of the current literature. In-depth comparisons are drawn amongst 140 published designs (both academic and industrial) and the associated performance trade-offs are characterised, discussed and illustrated. Seven key performance characteristics are described, namely their processing throughput, latency, hardware resource requirements, error correction capability, processing energy efficiency, bandwidth efficiency and flexibility. We offer recommendations that will facilitate fairer comparisons of future designs, as well as opportunities for improving the design of FPGA-based LDPC decoder