FPGA implementation of low complexity LDPC iterative decoder

Low-density parity-check (LDPC) codes, proposed by Gallager, emerged as a class of codes which can yield very good performance on the additive white Gaussian noise channel as well as on the binary symmetric channel. LDPC codes have gained lots of importance due to their capacity achieving property and excellent performance in the noisy channel. Belief propagation (BP) algorithm and its approximations, most notably min-sum, are popular iterative decoding algorithms used for LDPC and turbo codes. The trade-off between the hardware complexity and the decoding throughput is a critical factor in the implementation of the practical decoder. This article presents introduction to LDPC codes and its various decoding algorithms followed by realisation of LDPC decoder by using simplified message passing algorithm and partially parallel decoder architecture. Simplified message passing algorithm has been proposed for trade-off between low decoding complexity and decoder performance. It greatly reduces the routing and check node complexity of the decoder. Partially parallel decoder architecture possesses high speed and reduced complexity. The improved design of the decoder possesses a maximum symbol throughput of 92.95 Mbps and a maximum of 18 decoding iterations. The article presents implementation of 9216 bits, rate-1/2, (3, 6) LDPC decoder on Xilinx XC3D3400A device from Spartan-3A DSP family.     

基于VHDL的TPC译码器设计

Turbo乘积码是一种性能卓越的前向纠错码,具有译码复杂度低,且在低信噪比时可以获得近似最优的性能。介绍基于Chase算法的Turbo乘积码软入软出（SISO）迭代译码算法,提出基于VHDL硬件描述语言的TPC译码器设计方案,并在FPGA芯片上进行了仿真和验证。仿真结果证明该译码器有很大的实用性和灵活性。     

一种低码率的LDPC码在LTE-A中的性能研究

本文通过分析LTE-Advanced系统中准循环LDPC码校验矩阵的构造方法,在不改变母码矩阵的基础上,采用一种灵活的扩展方法,构造了一种低码率的LDPC码。采用一种很实用的编码算法和差分译码算法,在MATLAB仿真平台下,比较了这种LDPC码和Turbo码的性能。结果表明：在短码情况下,这种LDPC码在低信噪比下性能略低于Turbo码,但随着信噪比的增加,LDPC码性能优于Turbo码;在长码情况下,LDPC码的性能明显优于Turbo码。为LTE-Advanced系统的信道编解码器的硬件设计提供了一套有效的编译码算法方案,具有较好的实用价值。     

800Mbps准循环LDPC码译码器的FPGA实现

本文提出了一种适用于准循环低密度校验码的低复杂度的高并行度译码器架构。通常准循环低密度校验码不适于设计有效的高并行度高吞吐量译码器。我们通过利用准循环低密度校验码的奇偶校验矩阵的结构特点,将其转化为块准循环结构,从而能够并行化处理译码算法的行与列操作。使用这个架构,我们在Xilinx Virtex-5 LX330 FPGA上实现了(8176,7154)有限几何LDPC码的译码器,在15次迭代的条件下其译码吞吐量达到800Mbps。      

High-throughput LDPC decoders

A high-throughput memory-efficient decoder architecture for low-density parity-check (LDPC) codes is proposed based on a novel turbo decoding algorithm. The architecture benefits from various optimizations performed at three levels of abstraction in system design-namely LDPC code design, decoding algorithm, and decoder architecture. First, the interconnect complexity problem of current decoder implementations is mitigated by designing architecture-aware LDPC codes having embedded structural regularity features that result in a regular and scalable message-transport network with reduced control overhead. Second, the memory overhead problem in current day decoders is reduced by more than 75% by employing a new turbo decoding algorithm for LDPC codes that removes the multiple checkto-bit message update bottleneck of the current algorithm. A new merged-schedule merge-passing algorithm is also proposed that reduces the memory overhead of the current algorithm for low to moderate-throughput decoders. Moreover, a parallel soft-input-soft-output (SISO) message update mechanism is proposed that implements the recursions of the Balh-Cocke-Jelinek-Raviv (BCJR) algorithm in terms of simple "max-quartet" operations that do not require lookup-tables and incur negligible loss in performance compared to the ideal case. Finally, an efficient programmable architecture coupled with a scalable and dynamic transport network for storing and routing messages is proposed, and a full-decoder architecture is presented. Simulations demonstrate that the proposed architecture attains a throughput of 1.92 Gb/s for a frame length of 2304 bits, and achieves savings of 89.13% and 69.83% in power consumption and silicon area over state-of-the-art, with a reduction of 60.5% in interconnect length.     

A Memory Efficient Partially Parallel Decoder Architecture for Quasi-Cyclic LDPC Codes

This paper presents a memory efficient partially parallel decoder architecture suited for high rate quasi-cyclic low-density parity-check (QC-LDPC) codes using (modified) min-sum algorithm for decoding. In general, over 30% of memory can be saved over conventional partially parallel decoder architectures. Efficient techniques have been developed to reduce the computation delay of the node processing units and to minimize hardware overhead for parallel processing. The proposed decoder architecture can linearly increase the decoding throughput with a small percentage of extra hardware. Consequently, it facilitates the applications of LDPC codes in area/power sensitive high-speed communication systems     

IEEE802.16e标准LDPC译码器设计与实现

LDPC码自在上个世纪90年代被重新发现以来,以其接近香农极限的差错控制性能,以及译码复杂度低、吞吐率高的优点引起了人们的关注,成为继Turbo码之后信道编码界的又一研究热点。利用FPGA设计并实现了一种基于IEEE802.16e标准的LDPC码译码器。该译码器采用偏移最小和（Offset Min-Sum）算法,其偏移因子β取值为0.125,具有接近置信传播（Belief Propagation）算法浮点的性能。译码器在结构上采用了部分并行结构,可以灵活支持标准中定义的所有码率和码长的LDPC码的译码。此外,该译码器还支持对连续输入的数据块进行处理,并具有动态停止迭代功能。硬件综合结果表明,该译码器工作频率为150MHz时,固定15次迭代,最低可达到95Mb/s的译码吞吐率,完全满足802.16e标准的要求。     

适于分层译码算法的LDPC码构造方法

The layered decoding algorithm has been widely used in the implementation of Low Density Parity Check (LDPC) decoders, due to its high convergence speed. However, the pipeline operation of the layered decoder may introduce memory access conflicts, which heavily deteriorates the decoder throughput. To essentially deal with the issue of memory access conflicts, we propose a construction algorithm of LDPC codes, to which a constraint condition is added in the Progressive Edge-Growth (PEG) algorithm. The constraint condition can guarantee that for our constructed LDPC codes, the sets of all the variable nodes connected to the consecutive layers do not share any common variable node, which can avoid the memory access conflicts. Simulation results show that the performance of our constructed LDPC codes is close to the several other LDPC codes adopted in wireless standards. Moreover, compared with the decoder for IEEE 802. 16e LDPC codes, the throughput of our LDPC decoder has large improvement, while the chip resource consumption is unchanged. Thus, our constructed LD-PC codes can be adopted in the high-speed transmission.     

LDPC码的改进译码算法与快速硬件实现

基于Impulse C语言对LDPC码的改进译码算法进行了研究与编程实现,分别进行该算法的CoDeveloper桌面仿真和生成的硬件VHDL代码的ISE综合仿真.最后在Xilinx Virtex-2 XC2V2000-4bf957芯片上完成了码长为4 000、码率为0.5的(3,6)码译码器的快速FPGA实现.结果表明,当工作时钟为50 MHz,最大迭代次数为20次时,译码器的译码速率超过70 Mbit/s,硬件资源分配合理.     

A SiGe BiCMOS analog SISO decoder with I/O interface

Although recent implementations of analog iterative decoders have proven their potential for higher decoding speed and less power consumption than their digital counterparts, the CMOS or conventional BiCMOS technologies used so far seem to be incapable to cope with the need for high throughput that high-speed applications require. Within this context this work presents the design and test results of a high-speed analog SISO (Soft-Input Soft-Output) channel decoder for an 8-bit trellis code by exploiting the high-speed features of SiGe heterojunction bipolar transistors (HBTs). It is one of the first successful implementations of an error-correcting decoder in SiGe BiCMOS technology, which incorporates a high-speed I/O interface. A high-level model of the mismatch effects indicates that there is no significant performance penalty. Moreover, simulations and performance evaluations of an analog Turbo decoder based on the designed SISO decoder are provided. Even though the IC of the SISO module was tested at a throughput up to 3 Mbps, simulation results show that the decoder is capable to operate at 50 Mbps. The measured power consumption is 860 mW and the die area is 3.4 × 3 mm².     

Optimal Overlapped Message Passing Decoding of Quasi-Cyclic LDPC Codes

Efficient hardware implementation of low-density parity-check (LDPC) codes is of great interest since LDPC codes are being considered for a wide range of applications. Recently, overlapped message passing (OMP) decoding has been proposed to improve the throughput and hardware utilization efficiency (HUE) of decoder architectures for LDPC codes. In this paper, we first study the scheduling for the OMP decoding of LDPC codes, and show that maximizing the throughput gain amounts to minimizing the intra- and inter-iteration waiting times. We then focus on the OMP decoding of quasi-cyclic (QC) LDPC codes. We propose a partly parallel OMP decoder architecture and implement it using FPGA. For any QC LDPC code, our OMP decoder achieves the maximum throughput gain and HUE due to overlapping, hence has higher throughput and HUE than previously proposed OMP decoders while maintaining the same hardware requirements. We also show that the maximum throughput gain and HUE achieved by our OMP decoder are ultimately determined by the given code. Thus, we propose a coset-based construction method, which results in QC LDPC codes that allow our optimal OMP decoder to achieve higher throughput and HUE.     

Unified Convolutional/Turbo Decoder Design Using Tile-Based Timing Analysis of VA/MAP Kernel

To satisfy the advanced forward-error-correction (FEC) standards, in which the Convolutional code and Turbo code may co-exit, a prototype design of a unified Convolutional/Turbo decoder is proposed. In this paper, we systematically analyze the timing charts of both the Viterbi algorithm and the MAP algorithm. Then, three techniques, including Distribution, Pointer, and Parallel schemes, are introduced; they can be used as flexible tools in timing-chart analysis to either reduce memory size or to increase throughput rate. Furthermore, we propose a tile-based methodology to analyze the key features of timing charts, such as computing/memory units and hardware utilization. On the basis of the timing analysis, we developed a VA/MAP timing chart that has three modes (VA mode, MAP mode, and concurrent VA/MAP mode) by complementing the idle time of both VA and MAP decoding procedures. The new combined timing analysis helps us for constructing a unified component decoder with near 100% utilization rate of the processing element (PE) in both VA/MAP decoding functions.      

TURBO码中的交织器设计及其改进

Turbo码是近年来提出的一种信道编码.该系统在编码时采用并行的反馈系统卷积码(RSC).在编码的同时,对原始信息和经过交织(interleave)乱序的信息进行编码.Turbo码的解码一般采用软输入软输出解码器(SISO).其解码算法主要有SOVA、MAP以及改进的LOGMAN算法.Turbo码的编解码中,交织器的性能是一个关键问题.文章对交织器的设计和各种交织器的性能进行了探讨,并提出了一种易于硬件实现的交织器设计方法.     

Low Complexity Decoder Architecture for Low-Density Parity-Check Codes

In this paper, we propose a low complexity decoder architecture for low-density parity-check (LDPC) codes using a variable quantization scheme as well as an efficient highly-parallel decoding scheme. In the sum-product algorithm for decoding LDPC codes, the finite precision implementations have an important tradeoff between decoding performance and hardware complexity caused by two dominant area-consuming factors: one is the memory for updated messages storage and the other is the look-up table (LUT) for implementation of the nonlinear function Ψ(x). The proposed variable quantization schemes offer a large reduction in the hardware complexities for LUT and memory. Also, an efficient highly-parallel decoder architecture for quasi-cyclic (QC) LDPC codes can be implemented with the reduced hardware complexity by using the partially block overlapped decoding scheme and the minimized power consumption by reducing the total number of memory accesses for updated messages. For (3, 6) QC LDPC codes, our proposed schemes in implementing the highly-parallel decoder architecture offer a great reduction of implementation area by 33% for memory area and approximately by 28% for the check node unit and variable node unit computation units without significant performance degradation. Also, the memory accesses are reduced by 20%.     

中长帧非规则LDPC码译码器的FPGA实现

LDPC(低密度奇偶校验码)是一种优秀的线性分组码,是目前距香农限最近的一类纠错编码。与Turbo码相比,LDPC码能得到更高的译码速度和更好的误码率性能,从而被认为是下一代通信系统和磁盘存储系统中备选的纠错编码。简要介绍了适于硬件实现的LDPC码译码算法,并基于软判决译码规则,使用Verilog硬件描述语言,在X ilinx V irtex2 6000 FPGA上实现了码率为1/2、帧长504bit的非规则LDPC码译码器。     

Efficient hardware implementation of a highly-parallel 3GPP LTE/LTE-advance turbo decoder

We present an efficient VLSI architecture for 3GPP LTE/LTE-Advance Turbo decoder by utilizing the algebraic-geometric properties of the quadratic permutation polynomial (QPP) interleaver. The high-throughput 3GPP LTE/LTE-Advance Turbo codes require a highly-parallel decoder architecture. Turbo interleaver is known to be the main obstacle to the decoder parallelism due to the collisions it introduces in accesses to memory. The QPP interleaver solves the memory contention issues when several MAP decoders are used in parallel to improve Turbo decoding throughput. In this paper, we propose a low-complexity QPP interleaving address generator and a multi-bank memory architecture to enable parallel Turbo decoding. Design trade-offs in terms of area and throughput efficiency are explored to find the optimal architecture. The proposed parallel Turbo decoder has been synthesized, placed and routed in a 65-nm CMOS technology with a core area of 8.3 mm² and a maximum clock frequency of 400 MHz. This parallel decoder, comprising 64 MAP decoder cores, can achieve a maximum decoding throughput of 1.28 Gbps at 6 iterations     

一种低译码复杂度的Turbo架构LDPC码

针对低密度奇偶校验(LDPC)码较大的译码复杂度和RAM占用,该文提出了一种低译码复杂度的Turbo架构LDPC码并行交织级联Gallager码 (Parallel Interleaved Concatenated Gallager Code,PICGC)。该文给出了PICGC的设计方法和编译码算法,并分析比较了PICGC译码器与LDPC译码器所需的RAM存储量,推导出RAM节省比的上界。理论分析和仿真结果表明,PICGC以纠错性能略微降低为代价,有效地降低译码复杂度和RAM存储量,且译码时延并未增加,是一种有效且易于实现的信道编码方案。     

Memory-efficient sum-product decoding of LDPC codes

Low-density parity-check (LDPC) codes perform very close to capacity for long lengths on several channels. However, the amount of memory (fixed-point numbers that need to be stored) required for implementing the message-passing algorithm increases linearly as the number of edges in the graph increases. In this letter, we propose a decoding algorithm for decoding LDPC codes that reduces the memory requirement at the decoder. The proposed decoding algorithm can be analyzed using density evolution; further, we show how to design good LDPC codes using this. Results show that this algorithm provides almost the same performance as the conventional sum-product decoding of LDPC codes.     

Parallel High Throughput Soft-Output Sphere Decoding Algorithm

Multiple-Input-Multiple-Output communication systems demand fast sphere decoding with high performance. To speed up the computation, we propose a scheme with multiple fixed complexity sphere decoders to construct a parallel soft-output fixed complexity sphere decoder (PFSD). The proposed decoder is highly parallel and has performance comparable to soft-output list fixed complexity sphere decoder (LFSD) and K-best sphere decoder. In addition, we propose a parallel QR decomposition algorithm to lower the preprocessing overhead, and a low complexity LLR algorithm to allow parallel update of LLR values. We demonstrate that the PFSD algorithm can increase the throughput and reduce bit error rate of a soft-output solution in a 4 × 4 16-QAM system, and has superior performance compared to other soft decoders with comparable throughput and computation complexity. The PFSD algorithm has been mapped onto Xilinx XC4VLX160 FPGA. The resulting PFSD decoder can achieve up to 75 Mbps throughput for 4 × 4 64-QAM configuration at 100MHz with low control overhead.