Reformulated Inversionless Berlekamp-Massey Research Articles

A 124-Gb/s Decoder for Generalized Integrated Interleaved Codes

Generalized integrated interleaved (GII) codes have attracted much attention in distributed storage systems since they can reduce the overall redundancy by creating redundancy shared by the interleaves. The Berlekamp-Massey (BM) algorithm makes the GII decoding efficient by reusing the preceding results at each decoding stage. However, it also forms the speed bottleneck of GII decoders. The reformulated inversionless Berlekamp-Massey (riBM) algorithm is well known for its short critical path, but it is not generally suitable for GII decoding since its polynomials are difficult to be reused directly. In this paper, we address this issue by reinitializing the polynomials and propose a riBM-based GII decoding algorithm. In our simulations, slight performance degradation induced by the first-layer miscorrection is observed in the high signal-to-noise ratio (SNR) region. Hence, a subtle method is introduced to handle the miscorrected interleaves. Furthermore, the hardware architecture of the proposed decoding algorithm is developed and a high throughput decoder for the given example GII code is implemented. The synthesis results under TSMC 28-nm technology show that the decoder can achieve a throughput of up to 124 Gb/s. Moreover, the decoder has been implemented into a field-programmable gate array (FPGA) to validate its error-correction performance.

Efficient Berlekamp-Massey Algorithm and Architecture for Reed-Solomon Decoder

This paper presents a novel area-efficient key equation solver (KES) architecture for the syndrome-based Reed-Solomon (RS) decoders. We develop the compensated simplified reformulated inversionless Berlekamp-Massey (CS-RiBM) algorithm, which is proved to successfully remove unnecessary computations in the conventional reformulated inversionless Berlekamp-Massey (RiBM) algorithm with simple compensation. The proposed algorithm results in a simplified KES architecture using much fewer processing elements and can be implemented by a homogenous systolic architecture. The RS (255, 239) and RS (255, 223) decoders using the CS-RiBM architecture have been designed and synthesized with SMIC 0.18 μm CMOS technology library. The synthesis results, excluding FIFO stacks, show that the CS-RiBM architecture can reduce 14 to 29 % area compared with the prior related architectures based on the Berlekamp-Massey (BM) and modified Euclidean (ME) algorithms. The proposed RS decoders achieve similarly high throughput to the RS decoders using the RiBM architecture with lower hardware complexity and are 17 to 22 % more efficient. Higher efficiency is achievable as the error-correcting capability of the RS code increases.

RS码仿真与基于RiBM算法的硬件实现

To improve communication quality and meet the reliability requirement of data transmission,the Bit Error Rate(BER) performance of Reed-Solomon(RS) codes is analyzed,and a RS(15,9) hardware decoder based on Reformulated Inversionless Berlekamp-Massey(RiBM) algorithm is proposed.The decoder operates in pipeline architecture,and its key equation is resolved by the RiBM algorithm.On that basis,an atmospheric laser communication system is simulated by adding Additive White Gaussian Noise(AWGN) in a fiber,and it is tested on a Field Programmable Gate Array(FPGA) platform.The experimental result shows that decoding speed can be up to 1.11 Gbit/s,as 3.54 times as that of Altera′s IP core.The RiBM algorithm has advantages of low hardware complexity and short critical path delay,and can meet the demands of the decoding system.

New Cost-Effective Simplified Euclid’s Algorithm for Reed-Solomon Decoders

This paper proposes a cost-effective simplified Euclid's (SE) algorithm for Reed-Solomon decoders, which can replace the existing modified Euclid's (ME) algorithm. The new proposed SE algorithm, using new initial conditions and polynomials, can significantly reduce the computation complexity compared with the existing ME and reformulated inversionless Berlekamp-Massey (RiBM) algorithms, since it has the least number of coefficients in the new initial conditions. Thus, the proposed SE architecture, consisting of only 3t basic cells, has the smallest area among the existing key solver blocks, where t means the error correction capability. In addition, the SE architecture requires only the latency of 2t clock cycles to solve the key equation without initial latency. The proposed RS decoder has been synthesized using the 0.18 μm Samsung cell library, and the gate count of the RS decoder, excluding FIFO memory, is only 40,136 for the (255, 239, 8) RS code.

High-Speed Low-Complexity Reed-Solomon Decoder using Pipelined Berlekamp-Massey Algorithm and Its Folded Architecture

This paper presents a high-speed lowcomplexity pipelined Reed-Solomon (RS) (255,239) decoder using pipelined reformulated inversionless Berlekamp-Massey (pRiBM) algorithm and its folded version (PF-RiBM). Also, this paper offers efficient pipelining and folding technique of the RS decoders. This architecture uses pipelined Galois-Field (GF) multipliers in the syndrome computation block, key equation solver (KES) block, Forney block, Chien search block and error correction block to enhance the clock frequency. A high-speed pipelined RS decoder based on the pRiBM algorithm and its folded version have been designed and implemented with 90-㎚ CMOS technology in a supply voltage of 1.1 V. The proposed RS(255,239) decoder operates at a clock frequency of 700 ㎒ using the pRiBM architecture and also operates at a clock frequency of 750 ㎒ using the PF-RiBM, respectively. The proposed architectures feature high clock frequency and low-complexity.

The Implementation and Verification of RS(255, 223) Decoder According to CCSDS Specification

RS(Reed-Solomon)码是差错控制领域中一种性能优异的非二进制分组循环码,由于它具有很强的随机错误和突发错误的纠错能力,被CCSDS,NASA,ESA等空间组织接受,广泛应用于深空探测中.本文采用改进的Berlekamp算法,用FPGA实现了符合CCSDS标准的RS(255,223)码译码器;介绍了该译码器的实现流程、性能测试方法和基于PCI总线接口的测试平台;给出了测试结果,并且对理论上RS(255,223)译码器的误码性能与实际测试的误码率结果进行了比较和分析.验证结果证明该译码器能工作在400 Mbps以上的码率,使用FPGA资源180 000门,译码效果与理论上译码效果一致.