Feedback Codes Achieving the Capacity of the Z-Channel

Tallini, Luca G.; Al-Bassam, S.; Bose, B.

doi:10.1109/tit.2007.915919

Cited by 27 publications

(15 citation statements)

References 6 publications

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“…The work most closely related to what we discuss here is that of Bracher-Lapidoth [2], where the zero-error feedback capacity of state-dependent channels was determined, under the assumptions that fixed-length encoding is being used and that state information is available only at the encoder. We also mention the works of Zhao-Permuter [18], where the authors gave a characterization of the zero-error feedback capacity under fixed-length encoding for channels with state information at both the encoder and the decoder (but in which the state process is not necessarily memoryless and is even allowed to depend on the channel inputs), and Tallini-Al-Bassam-Bose [16], where zero-error VLF communication over the binary Z-channel was studied.…”

Section: Zero-error Capacity: Variable-length Codesmentioning

confidence: 99%

Fundamental Limits of Communication Over State-Dependent Channels With Feedback

Kovačević

Wang

Tan

2019

IEEE Trans. Commun.

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The fundamental limits of communication over state-dependent discrete memoryless channels with noiseless feedback are studied, under the assumption that the communicating parties are allowed to use variable-length coding schemes. Various cases are analyzed, with the employed coding schemes having either bounded or unbounded codeword lengths, and with state information revealed to the encoder and/or decoder in a strictly causal, causal, or non-causal manner. In each of these settings, necessary and sufficient conditions for positivity of the zero-error capacity are obtained and it is shown that, whenever the zeroerror capacity is positive, it equals the conventional vanishingerror capacity. Moreover, it is shown that the vanishing-error capacity of state-dependent channels is not increased by the use of feedback and variable-length coding. Both these kinds of capacities of state-dependent channels with feedback are thus fully characterized.

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Section: Zero-error Capacity: Variable-length Codesmentioning

confidence: 99%

Fundamental Limits of Communication Over State-Dependent Channels With Feedback

Kovačević

Wang

Tan

2019

IEEE Trans. Commun.

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“…A special case of Figure 7. q-ary Z-channel model this channel with q = 2 is the binary Z-channel, which was extensively studied [14], [15]. Both the noisy typewriter channel and the binary Z-channel have analytic expressions for the channel capacity and for the corresponding input distributions.…”

Section: A Capacity and Capacity Achieving Distributionsmentioning

confidence: 99%

A Constrained Coding Scheme for Correcting Asymmetric Magnitude-1 Errors in $q$ -Ary Channels

Hemo

Cassuto

2018

IEEE Trans. Inform. Theory

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Abstract-We present a constraint-coding scheme to correct asymmetric magnitude-1 errors in multi-level non-volatile memories. For large numbers of such errors, the scheme is shown to deliver better correction capability compared to known alternatives, while admitting low-complexity of decoding. Our results include an algebraic formulation of the constraint, necessary and sufficient conditions for correctability, a maximum-likelihood decoder running in complexity linear in the alphabet size, and upper bounds on the probability of failing to correct t errors. Besides the superior rate-correction tradeoff, another advantage of this scheme over standard error-correcting codes is the flexibility to vary the code parameters without significant modifications.

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“…AsC, let T = 5 and the Reed-Solomon-like σ-code beC = C 1,z 5 of lengthñ = 12 with k = 8 information digits in Z Z 16 and r = n − k = 4 check digits in Z Z 13 . By addingr = 1 extra check digit in Z Z D , the following CW codes of length n = 13 with k = 8 information digits in Z Z 16 , r = 4 check digits in Z Z 13 andr = 1 check digit in Z Z D can be defined as in (9) for any w ∈ Z Z D .…”

Section: Ieee International Symposium On Information Theorymentioning

confidence: 99%

“…. , m−1} ⊆ IR and x = y, then the above model captures the model of (partial) unidirectional channel [1], [14], [3], [13], [4]. Practical examples of physical channel modeled as above are the multi-level flash memories [2], [9], [10] and the repetition channels [11].…”

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confidence: 99%

On L<inf>1</inf> metric asymmetric/unidirectional error control codes, constrained weight codes and σ-codes

Tallini

Bose

2013

2013 IEEE International Symposium on Information Theory

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The general theory on partially asymmetric (t−, t+)-EC/(d−, d+)-ED m-ary codes for the L1 distance is developed. In this metric, such codes are capable of correcting t− or less negative errors, detecting d− or less negative errors, correcting t+ or less positive errors, and simultaneously detecting d+ or less positive errors. Based on the elementary symmetric function, a wide class of these codes with efficient decoding algorithms are given. Let S(m, n, w, D) be the set of all the m-ary words of length n with real sum of their components being equal to w mod D. Any subset of S(m, n, w, D) is called m-ary constrained weight (CW) code of length n and is known to be a (D − 1)-UED code. Given a field, K, of prime characteristic p, some m-ary CW codes of length n ≤ |K| − 1 are defined. Such codes are (t−, t+)-EC/(d−, d+)-ED and have a redundancy of ρ(C) = n − log m |C| ≤ ρ(S(m, n, w, d + 1)) + t log m |K|, with t = min{t− + d+, d− + t+}, d = max{t− + d+, d− + t+} and w ∈ II N. In particular, for t ≤ p−1, a class of essentially linear and systematic (hence, easy to encode) m-ary (t−, t+)-EC/(d−, d+)-ED CW σ-codes with length n ≤ |K| + d/(m − 1) − 1, k ≤ |K| − t log m |K| − 1 information digits and n − k = t log m |K| + d/(m − 1) check digits are given. Also, some new hybrid partially asymmetric/unidirectional/symmetric error control codes are given and shown to be equivalent to the partially asymmetric (t−, t+)-EC/(d−, d+)-ED m-ary codes.

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Feedback Codes Achieving the Capacity of the Z-Channel

Cited by 27 publications

References 6 publications

Fundamental Limits of Communication Over State-Dependent Channels With Feedback

Fundamental Limits of Communication Over State-Dependent Channels With Feedback

A Constrained Coding Scheme for Correcting Asymmetric Magnitude-1 Errors in $q$ -Ary Channels

On L<inf>1</inf> metric asymmetric/unidirectional error control codes, constrained weight codes and σ-codes

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Feedback Codes Achieving the Capacity of the Z-Channel

Cited by 27 publications

References 6 publications

Fundamental Limits of Communication Over State-Dependent Channels With Feedback

Fundamental Limits of Communication Over State-Dependent Channels With Feedback

A Constrained Coding Scheme for Correcting Asymmetric Magnitude-1 Errors in $q$ -Ary Channels

On L<inf>1</inf> metric asymmetric/unidirectional error control codes, constrained weight codes and &#x03C3;-codes

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On L<inf>1</inf> metric asymmetric/unidirectional error control codes, constrained weight codes and σ-codes