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

	Document type :	Reports : Internal report
	Discipline(s) :	Engineering, computing & technology : Computer science
	Focus Areas :	Computational Sciences
	To cite this reference:	http://hdl.handle.net/10993/52096

Title :	Early-Stopped Approach and Analysis for the Berlekamp-Massey Algorithm
Language :	English
Author, co-author :	Chou, Hung-Pu [University of Luxembourg > Interdisciplinary Centre for Security, Reliability and Trust (SNT) > SigCom >]
	Hong-fu, Chou []
Publication date :	2022
Publisher :	Luxembourg University
City :	Luxembourg
Country :	Luxembourg
Keywords :	[en] BCH code ; BM algorithm ; low latency design
Abstract :	[en] 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.
Permalink :	http://hdl.handle.net/10993/52096

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