Codes in permutations and error correction for rank modulation

Barg, Alexander; Mazumdar, Arya

doi:10.1109/isit.2010.5513604

Cited by 56 publications

(146 citation statements)

References 12 publications

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“…An expression for K n (D) (and thus T n (D)) for D ≤ n appears in [10] (see [4] also). The following bound is weaker but sufficient in our context.…”

Section: Geometry Of Permutation Spacesmentioning

confidence: 99%

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A rate-distortion theory for permutation spaces

Wang¹,

Mazumdar

Wornell³

2013

2013 IEEE International Symposium on Information Theory

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Abstract-We investigate the lossy compression of the permutation space by analyzing the trade-off between the size of a source code and the distortion with respect to either Kendall tau distance or 1 distance of the inversion vectors. For both distortion measures, we characterize the rate-distortion functions and provide explicit code designs that achieve them. Finally, we provide bounds on the higher order terms in the codebook size when the distortion levels lead to degenerate code rates (0 or 1).

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“…An expression for K n (D) (and thus T n (D)) for D ≤ n appears in [10] (see [4] also). The following bound is weaker but sufficient in our context.…”

Section: Geometry Of Permutation Spacesmentioning

confidence: 99%

“…For example, some works focus on codes in S n with Hamming distance [1], [2], and some others investigate the error correction problem under metrics such as Chebyshev distance [3] and Kendall tau distance [4].…”

Section: Introductionmentioning

confidence: 99%

A rate-distortion theory for permutation spaces

Wang¹,

Mazumdar

Wornell³

2013

2013 IEEE International Symposium on Information Theory

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“…Apart from the natural sorting algorithms, Kendall tau distance has recently attracted substantial interest in the area of error-correcting codes for Flash memory [5], [6], Kendall tau distance is also a global measure of disarray that is very popular in statistics. It is closely related to the Spearman's footrule, as we will see next.…”

Section: Operational Meaning Of the Distortion Measuresmentioning

confidence: 99%

Lossy compression of permutations

Wang

Mazumdar

Wornell

2014

2014 IEEE International Symposium on Information Theory

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Abstract-We investigate the lossy compression of permutations by analyzing the trade-off between the size of a source code and the distortion with respect to Kendall tau distance, Spearman's footrule, Chebyshev distance and 1 distance of inversion vectors. We show that given two permutations, Kendall tau distance upper bounds the 1 distance of inversion vectors and a scaled version of Kendall tau distance lower bounds the 1 distance of inversion vectors with high probability, which indicates an equivalence of the source code designs under these two distortion measures. Similar equivalence is established for all the above distortion measures, every one of which has different operational significance and applications in ranking and sorting. These findings show that an optimal coding scheme for one distortion measure is effectively optimal for other distortion measures above.

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“…Alternatives such as low-density parity check (LDPC) decoding is applied with the aid of soft information to maximize the mutual information between the input and the output and enhance by that the accuracy of the read operation [4]. Rank modulation schemes address the writing asymmetry within memory where the relative charge among several cells is used to represent the information [5]. Moreover, dynamic threshold setting is employed in flash memories, where the threshold is not fixed, but rather recalculated at every read operation [6], [7].…”

Section: Introductionmentioning

confidence: 99%

Channel equalization techniques for non-volatile memristor memories

Naous

Zidan

Sultan

et al. 2016

2016 Annual Conference on Information Science and Systems (CISS)

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Abstract-Channel coding and information theoretic approaches have been utilized in conventional non-volatile memories to overcome their inherent design limitations of leakage, coupling and refresh rates. However, the continuous scaling and integration constraints set on the current devices directed the attention towards emerging memory technologies as suitable alternatives. Memristive devices are prominent candidates to replace the conventional electronics due to its non-volatility and small feature size. Nonetheless, memristor-based memories still encounter an accuracy limitation throughout the read operation addressed as the sneak path phenomenon. The readout data is corrupted with added distortion that increases significantly the bit error rate and jeopardizes the reliability of the read operation. A novel technique is applied to alleviate this distorting effect where the communication channel model is proposed for the memory array. Noise cancellation principles are applied with the aid of preset pilots to extract channel information and adjust the readout values accordingly. The proposed technique has the virtue of high speed, energy efficiency, and low complexity design while achieving high reliability and error-free decoding.

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Codes in permutations and error correction for rank modulation

Cited by 56 publications

References 12 publications

A rate-distortion theory for permutation spaces

A rate-distortion theory for permutation spaces

Lossy compression of permutations

Channel equalization techniques for non-volatile memristor memories

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