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193 results on '"Guillen i Fabregas, Albert"'

1. Generalized Random Gilbert-Varshamov Codes: Typical Error Exponent and Concentration Properties

Author

Truong, Lan V. and Guillen i Fabregas, Albert

Abstract

We find the exact typical error exponent of constant composition generalized random Gilbert-Varshamov (RGV) codes over discrete memoryless channels with generalized likelihood decoding. We show that the typical error exponent of the RGV ensemble is equal to the expurgated error exponent, provided that the RGV codebook parameters are chosen appropriately. We also prove that the random coding exponent converges in probability to the typical error exponent, and the corresponding non-asymptotic concentration rates are derived. Our results show that the decay rate of the lower tail is exponential while that of the upper tail is double exponential above the expurgated error exponent. The explicit dependence of the decay rates on the RGV distance functions is characterized.

Published
2024
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2. Concentration Properties of Random Codes

Author

Truong, Lan V., Cocco, Giuseppe, Font-Segura, Josep, and Guillen i Fabregas, Albert

Abstract

This paper shows that, for discrete memoryless channels, the error exponent of a randomly generated code with independent codewords converges in probability to its expectation—the typical error exponent. For high rates, the result follows from the fact that the random-coding error exponent and the sphere-packing error exponent coincide. For low rates, instead, the convergence is based on the fact that the union bound accurately characterizes the error probability. The paper also zooms into the behavior at asymptotically low rates, and shows that the normalized error exponent converges in distribution to the standard Gaussian or a Gaussian-like distribution. We also state several results on the convergence of the error probability and error exponent for generic ensembles and channels.

Published
2023
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9. A Sphere-Packing Error Exponent for Mismatched Decoding

Author

Asadi Kangarshahi, Ehsan and Guillen i Fabregas, Albert

Abstract

We derive a sphere-packing error exponent for coded transmission over discrete memoryless channels with a fixed decoding metric. By studying the error probability of the code over an auxiliary channel, we find a lower bound to the probability of error of mismatched decoding. The bound is shown to decay exponentially for coding rates smaller than a new upper bound to the mismatch capacity which is established in this paper. For rates higher than the new upper bound, the error probability is shown to be bounded away from zero. The new upper bound is shown to improve over previous upper bounds to the mismatch capacity.

Published
2023
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12. Low-density parity-check codes for nonergodic block-fading channels

Author

Boutros, Joseph Jean, Guillen i Fabregas, Albert, Biglieri, Ezio, and Zemor, Gilles

Subjects
Error-correcting codes -- Properties, Fading channels -- Design and construction, Fading channels -- Control, Maximum likelihood estimates (Statistics) -- Measurement
Published
2010

20. Bayesian M-Ary Hypothesis Testing: The Meta-Converse and Verdu-Han Bounds Are Tight

Author

Vazquez-Vilar, Gonzalo, Tauste Campo, Adria, Guillen I Fabregas, Albert, Martinez, Alfonso, Guillen i Fabregas, Albert [0000-0003-2795-1124], and Apollo - University of Cambridge Repository

Subjects
Electronic mail, Hypothesis testing, meta-converse, information spectrum, channel coding, Testing, Error probability, Random variables, Shannon theory, Channel coding, Bayes methods
Abstract

Two alternative exact characterizations of the minimum error probability of Bayesian M-ary hypothesis testing are derived. The first expression corresponds to the error probability of an induced binary hypothesis test and implies the tightness of the meta-converse bound by Polyanskiy et al.; the second expression is a function of an information-spectrum measure and implies the tightness of a generalized Verdú-Han lower bound. The formulas characterize the minimum error probability of several problems in information theory and help to identify the steps where existing converse bounds are loose. This work was supported in part by the European Research Council under Grant 259663, in part by the Spanish Ministry of Economy and Competitiveness under Grant FPDI-2013-18602, Grant RYC-2011-08150, and Grant TEC2012-38800-C03-03, and in part by the European Union’s 7th Framework Programme under Grant 303633 and Grant 329837.

Published
2016

34. Multi-Class Source-Channel Coding

Author

Bocharova, Irina E., primary, Guillen i Fabregas, Albert, additional, Kudryashov, Boris D., additional, Martinez, Alfonso, additional, Tauste Campo, Adria, additional, and Vazquez-Vilar, Gonzalo, additional

Published
2016
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50. Source-channel coding with multiple classes

Author

Bocharova, Irina E., primary, Guillen i Fabregas, Albert, additional, Kudryashov, Boris D., additional, Martinez, Alfonso, additional, Campo, Adria Tauste, additional, and Vazquez-Vilar, Gonzalo, additional

Published
2014
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