New single asymmetric error-correcting codes

Al-Bassam, S.; Venkatesan, R.; Almuhammadi, Sultan

doi:10.1109/18.623162

Cited by 17 publications

(9 citation statements)

References 9 publications

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“…The lower bound (14) in Corollary 2 is better than the lower bound (6) in Theorem 2. Note that for d 3 (n + 1) s [(n + 1) 2 0 1] r (n + 1) 2r+s 0 1 = (n + 1) d01 0 1 and the equality holds if and only if d = 3.…”

Section: Acknowledgmentmentioning

confidence: 99%

New lower bounds and constructions for binary codes correcting asymmetric errors

Ling

Xing

2003

IEEE Trans. Inform. Theory

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In this correspondence, we study binary asymmetric errorcorrecting codes. A general construction for binary asymmetric error-correcting codes is presented. We show that some previously known lower bounds for binary asymmetric error-correcting codes can be obtained from this general construction. Furthermore, some new lower bounds for binary asymmetric error-correcting codes are obtained from this general construction. These new lower bounds improve the existing ones.

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Section: Acknowledgmentmentioning

confidence: 99%

New lower bounds and constructions for binary codes correcting asymmetric errors

Ling

Xing

2003

IEEE Trans. Inform. Theory

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“…In addition, a large amount This work was supported in part by the NSF CAREER Award CCF-0747415, the NSF grant ECCS-0802107, and by an NSF-NRI award. This paper was presented in part at IEEE International Symposium on Information Theory (ISIT), St of efforts are contributed to the design of systematic codes [1], [3], constructing single or multiple error-correcting codes [2], [16], [17], increasing the lower bounds [7]- [9], [24] and applying LDPC codes in the context of asymmetric channels [21]. However, the existing approach for code construction is similar to the approach taken in the construction of symmetric error-correcting codes, namely, it assumes that every codeword could tolerate t asymmetric errors (or generally t 1 1 → 0 errors and t 2 0 → 1 errors).…”

Section: Introductionmentioning

confidence: 99%

Nonuniform Codes for Correcting Asymmetric Errors in Data Storage

Zhou

Jiang

Bruck

2013

IEEE Trans. Inform. Theory

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The construction of asymmetric error correcting codes is a topic that was studied extensively, however, the existing approach for code construction assumes that every codeword should tolerate t asymmetric errors. Our main observation is that in contrast to symmetric errors, asymmetric errors are content dependent. For example, in Z-channels, the all-1 codeword is prone to have more errors than the all-0 codeword. This motivates us to develop nonuniform codes whose codewords can tolerate different numbers of asymmetric errors depending on their Hamming weights. The idea in a nonuniform codes' construction is to augment the redundancy in a content-dependent way and guarantee the worst case reliability while maximizing the code size. In this paper, we first study nonuniform codes for Zchannels, namely, they only suffer one type of errors, say 1 → 0. Specifically, we derive their upper bounds, analyze their asymptotic performances, and introduce two general constructions. Then we extend the concept and results of nonuniform codes to general binary asymmetric channels, where the error probability for each bit from 0 to 1 is smaller than that from 1 to 0.

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“…Asymmetric error-correcting codes have been widely studied: In [2], Kløve summarized and presented several such codes. In addition, a large amount of effort is contributed to the design of systematic codes [3], [4], constructing single or multiple error-correcting codes [5], [6], increasing the lower bounds [7]- [10] and applying LDPC codes in the context of asymmetric channels [11].…”

Section: Introductionmentioning

confidence: 99%

Nonuniform codes for correcting asymmetric errors

Zhou

Jiang

Bruck

2011

2011 IEEE International Symposium on Information Theory Proceedings

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Abstract-Codes that correct asymmetric errors have important applications in storage systems, including flash memories and phase-change memories. The construction of asymmetric error correcting codes is a topic that was studied extensively, however, the existing approach for code construction is similar to the approach taken in the construction of symmetric error correcting codes, namely, it assumes that every codeword could sustain t asymmetric errors. Our main observation is that in contrast to symmetric errors, where the error probability of a codeword is context independent (since the error probability for 1s and 0s is identical), asymmetric errors are context dependent. For example, the all-1 codeword has a higher error probability than the all-0 codeword (since the only errors are 1 → 0). We call the existing codes uniform codes while we focus on the notion of nonuniform codes, namely, codes whose codewords can tolerate different numbers of asymmetric errors depending on their Hamming weights. We prove an almost explicit upper bound on the size of nonuniform asymmetric error correcting codes and present two general constructions. We also study the rate of nonuniform codes compared to uniform codes and show that there is a potential performance gain.

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New single asymmetric error-correcting codes

Cited by 17 publications

References 9 publications

New lower bounds and constructions for binary codes correcting asymmetric errors

New lower bounds and constructions for binary codes correcting asymmetric errors

Nonuniform Codes for Correcting Asymmetric Errors in Data Storage

Nonuniform codes for correcting asymmetric errors

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