Early-Stopped Technique for BCH Decoding Algorithm Under Tolerant Fault Probability

In this paper, a technique for the Berlekamp-Massey(BM) algorithm is provided to reduce the latency of decoding and save decoding power by early termination or early-stopped checking. We investigate the consecutive zero discrepancies during the decoding iteration and decide to early stop the decoding process. This technique is subject to decoding failure in exchange for the decoding latency. We analyze our proposed technique by considering the weight distribution of BCH code and estimating the bounds of undetected error probability as the event of enormous stop checking. The proposed method is effective in numerical results and the probability of decoding failure is lower than $10^{-119}$ for decoding 16383 code length of BCH codes. Furthermore, the complexity compared the conventional early termination method with the proposed approach for decoding the long BCH code. The proposed approach reduces the complexity of the conventional approach by up to 80\%. As a result, the FPGA testing on a USB device validates the reliability of the proposed method.Comment: 6 pages, 5 figure

Early-Stopped Approach and Analysis for the Berlekamp-Massey Algorithm

BCH codes are being widely used in commercial NAND flash controllers, and the decoding algorithm based on the Berlekamp-Massey (BM) algorithm is a classic solution for solving the key equation used for error correction. The latency of BM decoding is the bottleneck of the Bose-Chaudhuri Hocquenghem (BCH) decoder when correcting a high number of bit errors. However, the flash memory has an error distribution that degrades with usage: few errors occur in the new memory and a low number of errors occur within a code block. With usage, the system performance degrades and BM decoding needs t iterations in order to correct a larger number t of errors. In an attempt to improve the system performance for high speed applications, early termination of the BM decoding is necessary to overcome this degradation. In this paper, a practical solution for early termination checking for BM algorithm is provided. The analysis of proposed method is presented by means of considering the weight distribution of BCH code and deriving the probability of malfunction as the event of undetectable error. The proposed method is presented to be effective by the numerical results and the probability of malfunction for the proposed method is lower than 10−26. As a result, the FPGA testing on a USB device validate the reliability of the proposed method for applying to a commercial product

Early-Stopped Technique for BCH Decoding Algorithm Under Tolerant Fault Probability

In this paper, a technique for the Berlekamp Massey(BM) algorithm is provided to reduce the latency of decoding and save decoding power by early termination or early stopped checking. We investigate the consecutive zero discrepan cies during the decoding iteration and decide to early stop the decoding process. This technique is subject to decoding failure in exchange for the decoding latency. We analyze our propose d technique by considering the weight distribution of BCH code and estimating the bounds of undetected error probability as the event of enormous stop checking. The proposed method is effective in numerical results and the probability of decoding failure is lower than 10 −119 for decoding 16383 code length of BCH codes. Furthermore, the complexity compared the conventional early termination method with the proposed approach for decoding the long BCH code. The proposed approach reduces the complexity of the conventional approach by up to 80%. As a result, the FPGA testing on a USB device validates the reliability of the proposed metho

A Microprocessor based hybrid system for digital error correction

The design of a microprocessor based hybrid system for digital error correction is presented. It is shown that such a system allows for implementation of several cyclic codes at a variety of throughput rates providing variable degrees of error correction depending on current user requirements. The theoretical basis for encoding and decoding of binary BCH codes is reviewed. Design and implementation of system hardware and software are described. A method for injection of independent bit errors with controllable statistics into the system is developed, and its accuracy verified by computer simulation. This method of controllable error injection is used to test performance of the designed system. In analysis, these results demonstrate the flexibility of operation provided by the hybrid nature of the system. Finally, potential applications and modifications are presented to reinforce the wide applicability of the system described in this thesis