Minimum probability of error of list M-ary hypothesis testing

We study a variation of Bayesian M-ary hypothesis testing in which the test outputs a list of L candidates out of the M possible upon processing the observation. We study the minimum error probability of list hypothesis testing, where an error is defined as the event where the true hypothesis is not in the list output by the test. We derive two exact expressions of the minimum probability or error. The first is expressed as the error probability of a certain non-Bayesian binary hypothesis test and is reminiscent of the meta-converse bound by Polyanskiy, Poor and Verdú (2010). The second, is expressed as the tail probability of the likelihood ratio between the two distributions involved in the aforementioned non-Bayesian binary hypothesis test. Hypothesis testing, error probability, information theory.European Research Council (Grant 725411); Spanish Ministry of Economy and Competitiveness (Grant PID2020-116683GB-C22)

Extremes of error exponents

This paper determines the range of feasible values of standard error exponents for binary-input memoryless symmetric channels of fixed capacity C and shows that extremes are attained by the binary symmetric and the binary erasure channel. The proof technique also provides analogous extremes for other quantities related to Gallager's E 0 function, such as the cutoff rate, the Bhattacharyya parameter, and the channel dispersion.This work was supported in part by the International Joint Project 2008/R2 of the Royal Society, in part by the Australian Research Council under ARC Discovery Grant DP0986089, and in part by the European Research Council under ERC grant agreement 259663. A. Martinez was supported in part by the Ministry of Economy and Competitiveness (Spain) under Grant RYC-2011-08150 and in part by the European Union’s 7th Framework Programme (PEOPLE-2011-CIG) under Grant 303633

Asymptotics of the random coding error probability for constant-composition codes

Comunicació presentada a 2019 IEEE International Symposium on Information Theory (ISIT), celebrada del 7 al 12 de juliol de 2019 a Paris, França.Saddlepoint approximations to the error probability are derived for multiple-cost-constrained random coding ensembles where codewords satisfy a set of constraints. Constantcomposition inputs over a binary symmetric channel are studied as a particular case. For codewords with equiprobable empirical distribution, the analysis recovers the same error exponent and pre-exponential polynomial decay as the uniform i.i.d. ensemble and provides an explicit formula for the loss in prefactor (thirdorder term) incurred by the constant-composition ensemble.This work has been funded in part by the European Research Council under grant 725411, and by the Spanish Ministry of Economy and Competitiveness under grant TEC2016-78434-C3-1-R

Asymptotics of the error probability in quasi-static binary symmetric channels

Comunicació presentada a 2017 IEEE International Symposium on Information Theory (ISIT), celebrada del 25 al 30 de juny de 2017 a Aachen, Alemania.This paper provides an asymptotic expansion of the error probability, as the codeword length n goes to infinity, in quasi-static binary symmetric channels. After the leading term, namely the outage probability, the next two terms are found to be proportional to log n n and 1 n respectively. Explicit characterizations of the respective coefficients are given. The resulting expansion gives an approximation to the random-coding union bound, accurate even at small codeword lengths.This work has been funded in part by the European Research Council under ERC grant agreement 259663 and by the Spanish Ministry of Economy and Competitiveness under grants RYC-2011-08150, FJCI-2014-22747, and TEC2016-78434-C3-1-R

A Counter-example to the mismatched decoding converse for binary-input discrete memoryless channels

This paper studies the mismatched decoding problem for binary-input discrete memoryless channels. An example is provided for which an achievable rate based on superposition coding exceeds the Csiszár-Körner-Hui rate, thus providing a counter-example to a previously reported converse result. Both numerical evaluations and theoretical results are used in establishing this claim.This work was supported in part by the European Union Seventh Framework Programme under Grant 303633, in part by the European Research Council under Grant 259663, in part by the Spanish Ministry of Economy and Competitiveness under Grant RYC-2011-08150 and Grant TEC2012-38800-C03-03, and in part by the Israel Science Foundation under Grant 2013/919