Erasure, list, and detection zero-error capacities for low noise and a relation to identification

Ahlswede, Rudolf; Cai, Ning; Zhang, Zhen

doi:10.1109/18.481778

Cited by 38 publications

(26 citation statements)

References 11 publications

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“…In his celebrated paper [3], Forney extended Gallager's bounding techniques [2] and found exponential error bounds for the ensemble performance of optimum generalized decoding rules that include the options of erasure, variable size lists, and decision feedback (see also later studies, e.g., [1], [4], [5], [6], [8], and [10]). …”

Section: Introductionmentioning

confidence: 99%

“…1 As can be seen, the computation of E 1 (R, T ) involves an optimization over two auxiliary parameters, ρ and s, which in general requires a two-dimensional search over these two parameters by some method. This is different from Gallager's random coding error exponent function for ordinary decoding (without 1 Forney also provides improved (expurgated) exponents at low rates, but we will focus here solely on (1).…”

Section: Introductionmentioning

confidence: 99%

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Error Exponents of Erasure/List Decoding Revisited Via Moments of Distance Enumerators

Merhav

2008

IEEE Trans. Inform. Theory

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The analysis of random coding error exponents pertaining to erasure/list decoding, due to Forney, is revisited. Instead of using Jensen's inequality as well as some other inequalities in the derivation, we demonstrate that an exponentially tight analysis can be carried out by assessing the relevant moments of a certain distance enumerator. The resulting bound has the following advantages: (i) it is at least as tight as Forney's bound, (ii) under certain symmetry conditions associated with the channel and the random coding distribution, it is simpler than Forney's bound in the sense that it involves an optimization over one parameter only (rather than two), and (iii) in certain special cases, like the binary symmetric channel (BSC), the optimum value of this parameter can be found in closed form, and so, there is no need to conduct a numerical search. We have not found yet, however, a numerical example where this new bound is strictly better than Forney's bound. This may provide an additional evidence to support Forney's conjecture that his bound is tight for the average code. We believe that the technique we suggest in this paper can be useful in simplifying, and hopefully also improving, exponential error bounds in other problem settings as well.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Error Exponents of Erasure/List Decoding Revisited Via Moments of Distance Enumerators

Merhav

2008

IEEE Trans. Inform. Theory

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“…0, we see that in the minimization (2) V needs to be chosen so as to satisfy D(V kPjQ) = 0, equivalently V (yjx)Q(x) = P(yjx)Q(x) for all x 2 X and y 2 Y, and we get C 0`( 0 + ; P) max Q recovering the previously known lower bound for zero-undetectederror capacity C 0u [2]- [5].…”

Section: Characterization Of C 0fmentioning

confidence: 99%

Zero-error list capacities of discrete memoryless channels

Telatar¹

Proceedings of 1995 IEEE International Symposium on Information Theory

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Abstract-We define zero-error list capacities for discrete memoryless channels. We find lower bounds to, and a characterization of these capacities. As is usual for such zero-error problems in information theory, the characterization is not generally a single-letter one. Nonetheless, we exhibit a class of channels for which a single letter characterization exists. We also show how the computational cutoff rate relates to the capacities we have defined.Index Terms-Acyclic channels, cutoff rate, list decoding, zero-error list capacity, zero undetected-error capacity.

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“…In [1], Forney derived lower bounds on the random coding exponents associated with decoding rules that allow for erasure and list decoding (see also later related studies [2] - [7]). The channel model he considered was a single user discrete memoryless channel (DMC) where a codebook of block length n is randomly drawn with i.i.d.…”

Section: Introductionmentioning

confidence: 99%

Exact Random Coding Exponents for Erasure Decoding

Somekh-Baruch

Merhav

2011

IEEE Trans. Inform. Theory

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Abstract-Random coding of a channel with an erasure option is studied. By analyzing the large deviations behavior of the code ensemble, we obtain exact single-letter formulas for the error exponents in lieu of Forney's lower bounds. The analysis technique we use is based on an enhancement and specialization of tools for assessing the moments of certain distance enumerators, that were recently used for determining the exponential behavior of other communication systems. We specialize our results to the binary symmetric channel case with uniform random coding distribution and derive an explicit expression for the error exponent which, unlike Forney's bounds, does not involve optimization over two parameters. We also establish the fact that for the binary symmetric channel case with uniform random coding distribution, the difference between the exact error exponent corresponding to the probability of undetected decoding error and the error exponent corresponding to the erasure event is equal to the threshold parameter. Numerical calculations for the binary symmetric channel with uniform random coding distribution indicate that in this case Forney's bound coincides with the exact random coding exponent.

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Erasure, list, and detection zero-error capacities for low noise and a relation to identification

Cited by 38 publications

References 11 publications

Error Exponents of Erasure/List Decoding Revisited Via Moments of Distance Enumerators

Error Exponents of Erasure/List Decoding Revisited Via Moments of Distance Enumerators

Zero-error list capacities of discrete memoryless channels

Exact Random Coding Exponents for Erasure Decoding

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