Graph decomposition: A new key to coding theorems

Csiszár, Imre; Körner, János

doi:10.1109/tit.1981.1056281

Cited by 183 publications

(293 citation statements)

References 10 publications

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“…Equation (16) resembles the mismatched decoding error exponent of [20] for maximum-metric decoding, and (17) resembles the corresponding LM rate of Csiszár-Körner-Hui [20], [21]. More precisely, the latter are written as in (16)- (17) with the terms E[log q(X, Y )]−E P [log q(X, Y )]…”

Section: Tightness Via Primal-domain Analysismentioning

confidence: 99%

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The likelihood decoder: Error exponents and mismatch

Scarlett

Martinez

Fàbregas

2015

2015 IEEE International Symposium on Information Theory (ISIT)

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Abstract-This paper studies likelihood decoding for channel coding over discrete memoryless channels. It is shown that the likelihood decoder recovers the same random-coding error exponents as the maximum-likelihood decoder for i.i.d. and constantcomposition random codes. The role of mismatch in likelihood decoding is studied, and the notion of the mismatched likelihood decoder capacity is introduced. It is shown, both in the case of random coding and optimized codebooks, that the mismatched likelihood decoder can lead to strictly worse achievable rates and error exponents compared to the corresponding mismatched maximum-metric decoder.

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Section: Tightness Via Primal-domain Analysismentioning

confidence: 99%

“…Combining these observations with (20), recalling that P XY denotes the joint type of (x, y), and using the standard property of types [10, Ch. 2]…”

Section: Tightness Via Primal-domain Analysismentioning

confidence: 99%

The likelihood decoder: Error exponents and mismatch

Scarlett

Martinez

Fàbregas

2015

2015 IEEE International Symposium on Information Theory (ISIT)

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“…8, which employed the method of types 10,11,22,33 . In the present case, second-order (Markov) types rather than the usual types are used.…”

Section: B the Methods Of Typesmentioning

confidence: 99%

“…From each of the d n−k cosets of L ⊥ in F 2n , select a vector that minimizes H c (M x ), i.e., a vector x satisfying H c (M x ) ≤ H c (M y ) for any y in the coset. This selection uses the idea of the minimum entropy decoder known in the classical information theory literature 33 .…”

Section: Proof Of Theoremmentioning

confidence: 99%

A lower bound on the quantum capacity of channels with correlated errors

Hamada¹

2002

Journal of Mathematical Physics

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The highest fidelity of quantum error-correcting codes of length n and rate R is proven to be lower bounded by 1 − exp[−nE(R) + o(n)] for some function E(R) on noisy quantum channels that are subject to not necessarily independent errors. The E(R) is positive below some threshold R 0 , which implies R 0 is a lower bound on the quantum capacity. This work is an extension of the author's previous works [M. Hamada, Phys. Rev. A, 65, 052305 (2002), e-Print quant-ph/0109114, LANL, 2001, and M. Hamada, e-Print quant-ph/0112103, LANL, 2001], which presented the bound for channels subject to independent errors, or channels modeled as tensor products of copies of a completely positive linear map. The relation of the channel class treated in this paper to those in the previous works are similar to that of Markov chains to sequences of independent identically distributed random variables.

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“…The material in this paper was presented in part at the Information Theory and Applications conference, San Diego, and also at the Conference on Information Sciences and Systems, the John Hopkins University, Baltimore, 2009. with α-decoding. We present our results in the format given in [25]. This technique also gives upper bounds on the ensemble averages.…”

Section: Introductionmentioning

confidence: 99%

Error Exponent for Multiple Access Channels: Upper Bounds

Nazari¹,

Pradhan

Anastasopoulos

2015

IEEE Trans. Inform. Theory

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A unified framework to obtain all known lower bounds (random coding, typical random coding and expurgated bound) on the reliability function of a point-to-point discrete memoryless channel (DMC) is presented. By using a similar idea for a two-user discrete memoryless (DM) multiple-access channel (MAC), three lower bounds on the reliability function are derived. The first one (random coding) is identical to the best known lower bound on the reliability function of DM-MAC. It is shown that the random coding bound is the performance of the average code in the constant composition code ensemble. The second bound (Typical random coding) is the typical performance of the constant composition code ensemble. To derive the third bound (expurgated), we eliminate some of the codewords from the codebook with larger rate. This is the first bound of this type that explicitly uses the method of expurgation for MACs. It is shown that the exponent of the typical random coding and the expurgated bounds are greater than or equal to the exponent of the known random coding bounds for all rate pairs. Moreover, an example is given where the exponent of the expurgated bound is strictly larger. All these bounds can be universally obtained for all discrete memoryless MACs with given input and output alphabets.

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Graph decomposition: A new key to coding theorems

Cited by 183 publications

References 10 publications

The likelihood decoder: Error exponents and mismatch

The likelihood decoder: Error exponents and mismatch

A lower bound on the quantum capacity of channels with correlated errors

Error Exponent for Multiple Access Channels: Upper Bounds

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