scholarly journals Iterative Soft-Decision Decoding of Binary Cyclic Codes

2008 ◽  
Vol 4 (2) ◽  
pp. 142 ◽  
Author(s):  
Marco Baldi ◽  
Giovanni Cancellieri ◽  
Franco Chiaraluce
Keyword(s):  
Error Correction ◽  
Cyclic Codes ◽  
Error Correcting Codes ◽  
Parity Check ◽  
Soft Decision ◽  
Coding Gain ◽  
New Approach ◽  
Decoding Algorithms ◽  
Soft Decision Decoding ◽  
Hard Decision

Binary cyclic codes achieve good error correction performance and allow the implementation of very simpleencoder and decoder circuits. Among them, BCH codesrepresent a very important class of t-error correcting codes, with known structural properties and error correction capability. Decoding of binary cyclic codes is often accomplished through hard-decision decoders, although it is recognized that softdecision decoding algorithms can produce significant coding gain with respect to hard-decision techniques. Several approaches have been proposed to implement iterative soft-decision decoding of binary cyclic codes. We study the technique based on “extended parity-check matrices”, and show that such method is not suitable for high rates or long codes. We propose a new approach, based on “reduced parity-check matrices” and “spread parity-check matrices”, that can achieve better correction performance in many practical cases, without increasing the complexity.

Improving LDPC Decoding Performance for 3D TLC NAND Flash by LLR Optimization Scheme for Hard and Soft Decision

2022 ◽  
Vol 27 (1) ◽  
pp. 1-20
Author(s):  
Lanlan Cui ◽  
Fei Wu ◽  
Xiaojian Liu ◽  
Meng Zhang ◽  
Renzhi Xiao ◽  
...  
Keyword(s):  
Error Correction ◽  
Distribution Model ◽  
Quantization Scheme ◽  
Nand Flash ◽  
Soft Decision ◽  
Ldpc Decoding ◽  
Error Correction Capability ◽  
Soft Decision Decoding ◽  
Threshold Voltage Distribution ◽  
Hard Decision

Low-density parity-check (LDPC) codes have been widely adopted in NAND flash in recent years to enhance data reliability. There are two types of decoding, hard-decision and soft-decision decoding. However, for the two types, their error correction capability degrades due to inaccurate log-likelihood ratio (LLR) . To improve the LLR accuracy of LDPC decoding, this article proposes LLR optimization schemes, which can be utilized for both hard-decision and soft-decision decoding. First, we build a threshold voltage distribution model for 3D floating gate (FG) triple level cell (TLC) NAND flash. Then, by exploiting the model, we introduce a scheme to quantize LLR during hard-decision and soft-decision decoding. And by amplifying a portion of small LLRs, which is essential in the layer min-sum decoder, more precise LLR can be obtained. For hard-decision decoding, the proposed new modes can significantly improve the decoder’s error correction capability compared with traditional solutions. Soft-decision decoding starts when hard-decision decoding fails. For this part, we study the influence of the reference voltage arrangement of LLR calculation and apply the quantization scheme. The simulation shows that the proposed approach can reduce frame error rate (FER) for several orders of magnitude.

scholarly journals Baseline parity-check matrix for iterative soft-decision decoding of binary cyclic codes

2020 ◽  
Vol 14 (12) ◽  
pp. 1968-1974
Author(s):  
Oluwaseyi P. Babalola ◽  
Olayinka O. Ogundile ◽  
Daniel Jaco J. Versfeld
Keyword(s):  
Cyclic Codes ◽  
Parity Check ◽  
Soft Decision ◽  
Parity Check Matrix ◽  
Check Matrix ◽  
Soft Decision Decoding

scholarly journals Hamming Codes: Error Reducing Techniques

2021 ◽  
Vol 9 (11) ◽  
pp. 1972-1974
Author(s):  
Rohitkumar R Upadhyay
Keyword(s):  
Lower Bound ◽  
Error Correction ◽  
Coding Theory ◽  
Hamming Distance ◽  
Error Reduction ◽  
Error Correcting Codes ◽  
Significant Other ◽  
Hamming Codes ◽  
Decoding Algorithms ◽  
Reducing Properties

Abstract: Hamming codes for all intents and purposes are the first nontrivial family of error-correcting codes that can actually correct one error in a block of binary symbols, which literally is fairly significant. In this paper we definitely extend the notion of error correction to error-reduction and particularly present particularly several decoding methods with the particularly goal of improving the error-reducing capabilities of Hamming codes, which is quite significant. First, the error-reducing properties of Hamming codes with pretty standard decoding definitely are demonstrated and explored. We show a sort of lower bound on the definitely average number of errors present in a decoded message when two errors for the most part are introduced by the channel for for all intents and purposes general Hamming codes, which actually is quite significant. Other decoding algorithms are investigated experimentally, and it generally is definitely found that these algorithms for the most part improve the error reduction capabilities of Hamming codes beyond the aforementioned lower bound of for all intents and purposes standard decoding. Keywords: coding theory, hamming codes, hamming distance

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