Massively parallel implementation of cyclic LDPC codes on a general purpose graphic processing unit

2009 IEEE Workshop On Signal Processing Systems (SiPS) Tampere, Finland 2009-10-07 ~ 2009-10-09Simulation of low-density parity-check (LDPC) codes frequently takes several days, thus the use of general purpose graphics processing units (GPGPUs) is very promising. However, GPGPUs are designed for compute-intensive applications, and they are not optimized for data caching or control management. In LDPC decoding, the parity check matrix H needs to be accessed at every node updating process, and the size of H matrix is often larger than that of GPU on-chip memory especially when the code-length is long or the weight is high. In this work, the parity check matrix of cyclic or quasi-cyclic LDPC codes is greatly compressed by exploiting the periodic property of the matrix. In our experiments, the Compute Unified Device Architecture (CUDA) of Nvidia is used. With the (1057, 813) and (4161, 3431) projective geometry (PG)–LDPC codes, the execution speed of the proposed method is more than twice of the reference implementations that do not exploit the cyclic property of the parity check matrices

GPUs as Storage System Accelerators

Massively multicore processors, such as Graphics Processing Units (GPUs), provide, at a comparable price, a one order of magnitude higher peak performance than traditional CPUs. This drop in the cost of computation, as any order-of-magnitude drop in the cost per unit of performance for a class of system components, triggers the opportunity to redesign systems and to explore new ways to engineer them to recalibrate the cost-to-performance relation. This project explores the feasibility of harnessing GPUs' computational power to improve the performance, reliability, or security of distributed storage systems. In this context, we present the design of a storage system prototype that uses GPU offloading to accelerate a number of computationally intensive primitives based on hashing, and introduce techniques to efficiently leverage the processing power of GPUs. We evaluate the performance of this prototype under two configurations: as a content addressable storage system that facilitates online similarity detection between successive versions of the same file and as a traditional system that uses hashing to preserve data integrity. Further, we evaluate the impact of offloading to the GPU on competing applications' performance. Our results show that this technique can bring tangible performance gains without negatively impacting the performance of concurrently running applications.Comment: IEEE Transactions on Parallel and Distributed Systems, 201

New Algorithms for High-Throughput Decoding with Low-Density Parity-Check Codes using Fixed-Point SIMD Processors

Most digital signal processors contain one or more functional units with a single-instruction, multiple-data architecture that supports saturating fixed-point arithmetic with two or more options for the arithmetic precision. The processors designed for the highest performance contain many such functional units connected through an on-chip network. The selection of the arithmetic precision provides a trade-off between the task-level throughput and the quality of the output of many signal-processing algorithms, and utilization of the interconnection network during execution of the algorithm introduces a latency that can also limit the algorithm\u27s throughput. In this dissertation, we consider the turbo-decoding message-passing algorithm for iterative decoding of low-density parity-check codes and investigate its performance in parallel execution on a processor of interconnected functional units employing fast, low-precision fixed-point arithmetic. It is shown that the frequent occurrence of saturation when 8-bit signed arithmetic is used severely degrades the performance of the algorithm compared with decoding using higher-precision arithmetic. A technique of limiting the magnitude of certain intermediate variables of the algorithm, the extrinsic values, is proposed and shown to eliminate most occurrences of saturation, resulting in performance with 8-bit decoding nearly equal to that achieved with higher-precision decoding. We show that the interconnection latency can have a significant detrimental effect of the throughput of the turbo-decoding message-passing algorithm, which is illustrated for a type of high-performance digital signal processor known as a stream processor. Two alternatives to the standard schedule of message-passing and parity-check operations are proposed for the algorithm. Both alternatives markedly reduce the interconnection latency, and both result in substantially greater throughput than the standard schedule with no increase in the probability of error

연판정 오류정정을 위한 낮은 복잡도의 블록 터보부호 복호화 연구

학위논문 (박사)-- 서울대학교 대학원 : 전기·컴퓨터공학부, 2016. 8. 성원용.As the throughput needed for communication systems and storage devices increases, high-performance forward error correction (FEC), especially soft-decision (SD) based technique, becomes essential. In particular, block turbo codes (BTCs) and low-density parity check (LDPC) codes are considered as candidate FEC codes for the next generation systems, such as beyond-100Gbps optical networks and under-20nm NAND flash memory devices, which require capacity-approaching performance and very low error floor. The BTCs have definite strengths in diversity and encoding complexity because they generally employ a two-dimensional structure, which enables sub-frame level decoding for the row or column code-words. This sub-frame level decoding gives a strong advantage for parallel processing. The BTC decoding throughput can be improved by applying a low-complexity algorithm to the small level decoding or by running multiple sub-frame decoding modules simultaneously. In this dissertation, we develop high-throughput BTC decoding software that pursuits these advantages. The first part of this dissertation is devoted to finding efficient test patterns in the Chase-Pyndiah algorithm. Although the complexity of this algorithm linearly increases according to the number of the test patterns, it naively considers all possible patterns containing least reliable positions. As a result, consideration of one more position nearly doubles the complexity. To solve this issue, we first introduce a new position selection criterion that excludes some of the selected ones having a relatively large reliability. This technique excludes the selection of sufficiently reliable positions, which greatly reduces the complexity. Secondly, we propose a pattern selection scheme considering the error coverage. We define the error coverage factor that represents the influence on the error-correcting performance and compute it by analyzing error events. Based on the computed factor, we select the patterns with the greedy algorithm. By using these methods, we can flexibly balance the complexity and the performance. The second part of this dissertation is developing low-complexity soft-output processing methods needed for BTC decoding. In the Chase-Pyndiah algorithm, the soft-output is updated in two different ways according to whether competing code-words exist on the updating positions or not. If the competing code-words exist, the Euclidean distance between the soft-input signal and the code-words that are generated from the test patterns is used. However, the cost of distance computation is very high and linearly increases with the sub-frame length. We identify computationally redundant positions and optimize the computing process by ignoring them. If the competing ones do not exist, the reliability factor that should be pre-determined by an extensive search is demanded. To avoid this, we propose adaptive determination methods, which provides even better error-correcting performance. In addition, we investigate the Pyndiah's soft-output computation and find its drawbacks that appear during the approximation process. To remove the drawbacks, we replace the updating method of the positions that are expected to be seriously damaged by the approximation with the reliability factor-based one, which is much simpler, even though they have the competing words. This dissertation also develops a graphics processing unit (GPU) based BTC decoding program. In order to hide the latency of arithmetic and memory access operations, this software applies the kernel structure that processes multiple BTC-words and allocates multiple sub-frames to each thread-block. Global memory access optimization and data compression, which demands less shared memory space, are also employed. For efficient mapping of the Chase-Pyndiah algorithm onto GPUs, we propose parallel processing schemes employing efficient reduction algorithms and provide step-by-step parallel algorithms for the algebraic decoding. The last part of this dissertation is devoted to summarizing the developed decoding method and comparing it with the decoding of the LDPC convolutional code (CC), which is currently reported as the most powerful candidate for the 100Gbps optical network. We first investigate the complexity reduction and the error rate performance improvement of the developed method. Then, we analyze the complexity of the LDPC-CC decoding and compare it with the developed BTC decoding for the 20% overhead codes. This dissertation is intended to develop high-throughput SD decoding software by introducing complexity reduction techniques for the Chase-Pyndiah algorithm and efficient parallel processing methods, and to emphasize the competitiveness of the BTC. The proposed decoding methods and parallel processing algorithms verified in the GPU-based systems are also applicable to hardware-based ones. By implementing hardware-based decoders that employ the developed methods in this dissertation, significant improvements on the throughputs and the energy efficiency can be obtained. Moreover, thanks to the wide rate coverage of the BTC, the developed techniques can be applied to many high-throughput error correction applications, such as the next-generation optical network and storage device systems.Chapter 1 Introduction 1 1.1 Turbo Codes 1 1.2 Applications of Turbo Codes 4 1.3 Outline of the Dissertation 5 Chapter 2 Encoding and Iterative Decoding of Block Turbo Codes 7 2.1 Introduction 7 2.2 Encoding Procedure of Shortened-Extended BTCs 9 2.3 Scheduling Methods for Iterative Decoding 9 2.3.1 Serial Scheduling 10 2.3.2 Parallel Scheduling 10 2.3.3 Replica Scheduling 11 2.4 Elementary Decoding with Chase-Pyndiah Algorithm 13 2.4.1 Chase-Pyndiah Algorithm for Extended BTCs 13 2.4.2 Reliability Computation of the ML Code-Word 17 2.4.3 Algebraic Decoding for SEC and DEC BCH Codes 20 2.5 Issues of Chase-Pyndiah Algorithm 23 Chapter 3 Complexity Reduction Techniques for Code-Word Set Generation of the Chase-Pyndiah Algorithm 24 3.1 Introduction 24 3.2 Adaptive Selection of LRPs 25 3.2.1 Selection Constraints of LRPs 25 3.2.2 Simulation Results 26 3.3 Test Pattern Selection 29 3.3.1 The Error Coverage Factor of Test Patterns 30 3.3.2 Greedy Selection of Test Patterns 33 3.3.3 Simulation Results 34 3.4 Concluding Remarks 34 Chapter 4 Complexity Reduction Techniques for Soft-Output Update of the Chase-Pyndiah Algorithm 37 4.1 Introduction 37 4.2 Distance Computation 38 4.2.1 Position-Index List Based Method 39 4.2.2 Double Index Set-Based Method 42 4.2.3 Complexity Analysis 46 4.2.4 Simulation Results 47 4.3 Reliability Factor Determination 49 4.3.1 Refinement of Distance-Based Reliability Factor 51 4.3.2 Adaptive Determination of the Reliability Factor 51 4.3.3 Simulation Results 53 4.4 Accuracy Improvement in Extrinsic Information Update 54 4.4.1 Drawbacks of the Sub-Optimal Update 55 4.4.2 Low-Complexity Extrinsic Information Update 58 4.4.3 Simulation Results 59 4.5 Concluding Remarks 61 Chapter 5 High-Throughput BTC Decoding on GPUs 64 5.1 Introduction 64 5.2 BTC Decoder Architecture for GPU Implementations 66 5.3 Memory Optimization 68 5.3.1 Global Memory Access Reduction 68 5.3.2 Improvement of Global Memory Access Coalescing 68 5.3.3 Efficient Shared Memory Control with Data Compression 70 5.3.4 Index Parity Check Scheme 73 5.4 Parallel Algorithms with the CUDA Shuffle Function 77 5.5 Implementation of Algebraic Decoder 78 5.5.1 Galois Field Operations with Look-Up Tables 78 5.5.2 Error-Locator Polynomial Setting with the LUTs 81 5.5.3 Parallel Chien Search with the LUTs 84 5.6 Simulation Results 85 5.7 Concluding Remarks 89 Chapter 6 Competitiveness of BTCs as FEC codes for the Next-Generation Optical Networks 91 6.1 Introduction 91 6.2 The Complexity Reduction of the Modified Chase-Pyndiah Algorithm 92 6.2.1 Summary of the Complexity Reduction 92 6.2.2 The Error-Correcting Performance 94 6.3 Comparison of BTCs and LDPC-CCs 97 6.3.1 Complexity Analysis of the LDPC-CC Decoding 97 6.3.2 Comparison of the 20% Overhead BTC and LDPC-CC 100 6.4 Concluding Remarks 101 Chapter 7 Conclusion 102 Bibliography 105 국문 초록 113Docto

Tridimensional block multiword LDPC decoding on GPUs

[EN] In this paper, we describe a parallel algorithm for LDPC (Low Density Parity Check codes) decoding on a GPU (Graphics Processing Unit) using CUDA (Compute Unified Device Architecture). The strategy of the kernel grid and block design is shown and the multiword decoding operation is described using tridimensional blocks. The performance (speedup) of the proposed parallel algorithm is slightly better than the performance found in the literature when this is relatively good, and shows a great improvement in those cases with previously reported moderate or bad performance. © 2011 Springer Science+Business Media, LLC.This work was financially supported by the Spanish Ministerio de Ciencia e Innovación (Projects TIN2008-06570-C04-02, TEC2009-13741 and TEC2008-06787), Universidad Politécnica de Valencia through “Programa de Apoyo a la Investigación y Desarrollo (PAID-05-09)” and Generalitat Valenciana through project PROMETEO/2009/013.Martínez Zaldívar, FJ.; Vidal Maciá, AM.; González Salvador, A.; Almenar Terré, V. (2011). Tridimensional block multiword LDPC decoding on GPUs. Journal of Supercomputing. 58(3):314-322. https://doi.org/10.1007/s11227-011-0587-3S314322583Berrou C, Glavieux A, Thitimajshima P (1993) Near Shannon limit error-correcting coding and decoding: turbo-codes. In: International conference on communications, GenevaFalcão G, Sousa L, Silva V (2008) Massive parallel LDPC decoding on GPU. In: Proceedings of the 13th ACM SIGPLAN symposium on principles and practice of parallel programming, Salt Lake City, UT, USA, February 20–23, pp 83–90Falcão G, Silva V, Sousa L (2009) How GPUs can outperform ASICs for fast LDPC decoding. In: Proceedings of the 23rd international conference on supercomputing, Yorktown Heights, NY, USA, pp 390–399Falcão G, Sousa L, Silva V, Maurinho J (2009) Parallel LDPC decoding on the Cell/B.E. processor. In: Lecture notes in computer science, vol 5409. Springer, Berlin, pp 389–403Falcão G, Yamagiwa S, Silva V, Sousa L (2009) Parallel LDPC decoding on GPUs using a stream-based computing approach. J Comput Sci Technol 24(5):913–924Gallager RG (1963) Low density parity check codes. Ph.D. diss, MITKirk DB, Hwu WW (2010) Programming massively parallel processors. A hands on approach, NVidia. Morgan Kaufmann, San MateoMackay DJC, Neal RM (1996) Near Shannon limit performance of low density parity check codes. Electron Lett 32(18):1645–1646Richardson T, Urbanke R (2008) Modern coding theory. Cambridge University Press, CambridgeShannon C (1948) A mathematical theory of communication. Bell Syst Tech J 27:379–423 and 623–656Tanner R (1981) A recursive approach to low complexity codes. IEEE Trans Inf Theory 27(5):533–547Wang S, Cheng S, Wu Q (2008) A parallel decoding algorithm of LDPC codes using CUDA. In: Proc asilomar conference on signals, systems and computers, Pacific Grove, CA, Octobe