{"title":"Concatenated Coding for Multilevel Flash Memory with Low Error Correction Capabilities in Outer Stage","authors":"F. Taubin, A. Trofimov","doi":"10.15622/sp.2019.18.5.1149-1181","DOIUrl":null,"url":null,"abstract":"One of the approaches to organization of error correcting coding for multilevel flash memory is based on concatenated construction, in particular, on multidimensional lattices for inner coding. A characteristic feature of such structures is the dominance of the complexity of the outer decoder in the total decoder complexity. Therefore the concatenated construction with low-complexity outer decoder may be attractive since in practical applications the decoder complexity is the crucial limitation for the usage of the error correction coding. \nWe consider a concatenated coding scheme for multilevel flash memory with the Barnes-Wall lattice based codes as an inner code and the Reed-Solomon code with correction up to 4…5 errors as an outer one. \nPerformance analysis is fulfilled for a model characterizing the basic physical features of a flash memory cell with non-uniform target voltage levels and noise variance dependent on the recorded value (input-dependent additive Gaussian noise, ID-AGN). For this model we develop a modification of our approach for evaluation the error probability for the inner code. This modification uses the parallel structure of the inner code trellis which significantly reduces the computational complexity of the performance estimation. We present numerical examples of achievable recording density for the Reed-Solomon codes with correction up to four errors as the outer code for wide range of the retention time and number of write/read cycles.","PeriodicalId":53447,"journal":{"name":"SPIIRAS Proceedings","volume":"9 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2019-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"SPIIRAS Proceedings","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.15622/sp.2019.18.5.1149-1181","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 1
Abstract
One of the approaches to organization of error correcting coding for multilevel flash memory is based on concatenated construction, in particular, on multidimensional lattices for inner coding. A characteristic feature of such structures is the dominance of the complexity of the outer decoder in the total decoder complexity. Therefore the concatenated construction with low-complexity outer decoder may be attractive since in practical applications the decoder complexity is the crucial limitation for the usage of the error correction coding.
We consider a concatenated coding scheme for multilevel flash memory with the Barnes-Wall lattice based codes as an inner code and the Reed-Solomon code with correction up to 4…5 errors as an outer one.
Performance analysis is fulfilled for a model characterizing the basic physical features of a flash memory cell with non-uniform target voltage levels and noise variance dependent on the recorded value (input-dependent additive Gaussian noise, ID-AGN). For this model we develop a modification of our approach for evaluation the error probability for the inner code. This modification uses the parallel structure of the inner code trellis which significantly reduces the computational complexity of the performance estimation. We present numerical examples of achievable recording density for the Reed-Solomon codes with correction up to four errors as the outer code for wide range of the retention time and number of write/read cycles.
期刊介绍:
The SPIIRAS Proceedings journal publishes scientific, scientific-educational, scientific-popular papers relating to computer science, automation, applied mathematics, interdisciplinary research, as well as information technology, the theoretical foundations of computer science (such as mathematical and related to other scientific disciplines), information security and information protection, decision making and artificial intelligence, mathematical modeling, informatization.