The likelihood decoder: Error exponents and mismatch

Scarlett, Jonathan; Martinez, Alfonso; Fàbregas, Albert Guillén i

doi:10.1109/isit.2015.7282422

Cited by 23 publications

(33 citation statements)

References 23 publications

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“…In the matched setting, an alternative to maximum-likelihood decoding is stochastic likelihood decoding [95], in which each codeword is selected with probability proportional to its likelihood. In [72], ensemble-tight rates and error exponents were studied for a mismatched variant of this decoder in which the likelihood W n (y|x) is replaced by a single-letter decoding metric q n (x, y). These results were further generalized to certain multi-letter metrics in [60], where it was additionally shown that this decoder provides a novel approach to deriving expurgated error exponents.…”

Section: Other Decoding Methodsmentioning

confidence: 99%

Information-Theoretic Foundations of Mismatched Decoding

Scarlett,

Fàbregas,

Somekh-Baruch

et al. 2020

Preprint

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Shannon's channel coding theorem characterizes the maximal rate of information that can be reliably transmitted over a communication channel when optimal encoding and decoding strategies are used. In many scenarios, however, practical considerations such as channel uncertainty and implementation constraints rule out the use of an optimal decoder. The mismatched decoding problem addresses such scenarios by considering the case that the decoder cannot be optimized, but is instead fixed as part of the problem statement. This problem is not only of direct interest in its own right, but also has close connections with other long-standing theoretical problems in information theory.In this monograph, we survey both classical literature and recent developments on the mismatched decoding problem, with an emphasis on achievable random-coding rates for memoryless channels. We present two widely-considered achievable rates known as the generalized mutual information (GMI) and the LM rate, and overview their derivations and properties. In addition, we survey several improved rates via multi-user coding techniques, as well as recent developments and challenges in establishing converse bounds, and an analogous mismatched encoding problem in rate-distortion theory. Throughout the monograph, we highlight a variety of applications and connections with other prominent information theory problems.

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Section: Other Decoding Methodsmentioning

confidence: 99%

Information-Theoretic Foundations of Mismatched Decoding

Scarlett,

Fàbregas,

Somekh-Baruch

et al. 2020

Preprint

Self Cite

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“…we have the ordinary likelihood decoder in spirit of [13], [14], [16]. For a(P xy ) = β x∈X y∈YP xy (x, y) ln P (x|y),…”

Section: Notation Conventionsmentioning

confidence: 99%

“…The case of ordinary, deterministic MAP decoding is obtained again as of special case of (5) in the limit β → ∞. As in (13), when the objective function to be minimized over {Q XX ′ Y )}, contains a term like β · G(Q XX ′ Y ) (for some functional G(·)), then in the limit of β → ∞, it is replaced by a constraint of the form G(Q XX ′ Y ) ≤ 0.…”

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confidence: 99%

Ensemble Performance of Biometric Authentication Systems Based on Secret Key Generation

Merhav

2019

IEEE Trans. Inform. Theory

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We study the ensemble performance of biometric authentication systems, based on secret key generation, which work as follows. In the enrollment stage, an individual provides a biometric signal that is mapped into a secret key and a helper message, the former being prepared to become available to the system at a later time (for authentication), and the latter is stored in a public database. When an authorized user requests authentication, claiming his/her identity as one of the subscribers, s/he has to provide a biometric signal again, and then the system, which retrieves also the helper message of the claimed subscriber, produces an estimate of the secret key, that is finally compared to the secret key of the claimed user. In case of a match, the authentication request is approved, otherwise, it is rejected. Referring to an ensemble of systems based on Slepian-Wolf binning, we provide a detailed analysis of the false-reject and false-accept probabilities, for a wide class of stochastic decoders. We also comment on the security for the typical code in the ensemble.

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“…decoder achieves the optimal random coding exponent when α ∈ [α c , ∞] where α c ∈ [0, 1] depends on the given rate [41][42] [43]. α = 1 corresponds to likelihood decoder and α = ∞ corresponds to the maximum likelihood decoder.…”

Section: A Converse On the Error Exponent Of Weighted Samplingmentioning

confidence: 99%

Sharp Bounds for Mutual Covering

Liu

Yassaee

Verdú

2019

IEEE Trans. Inform. Theory

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A fundamental tool in network information theory is the covering lemma, which lower bounds the probability that there exists a pair of random variables, among a give number of independently generated candidates, falling within a given set. We use a weighted sum trick and Talagrand's concentration inequality to prove new mutual covering bounds. We identify two interesting applications: 1) When the probability of the set under the given joint distribution is bounded away from 0 and 1, the covering probability converges to 1 doubly exponentially fast in the blocklength, which implies that the covering lemma does not induce penalties on the error exponents in the applications to coding theorems. 2) Using Hall's marriage lemma, we show that the maximum difference between the probability of the set under the joint distribution and the covering probability equals half the minimum total variation distance between the joint distribution and any distribution that can be simulated by selecting a pair from the candidates. Thus we use the mutual covering bound to derive the exact error exponent in the joint distribution simulation problem. In both applications, the determination of the exact exponential (or doubly exponential) behavior relies crucially on the sharp concentration inequality used in the proof of the mutual covering lemma.Parts of the paper (mostly, Part 1) described in the abstract) were presented at ISIT 2017. 1 A single-shot formulation refers to the non-asymptotic setting where the random variables are not necessarily vectors with i.i.d. coordinates.Of course, the main contribution of the paper lies in the new arguments for bounding the covering and the sampling error, which are independent of the type of formulation we adopt.2 In contrast to the standard literature, we add the qualifier "unilateral" to differentiate the standard covering lemma with the mutual covering lemma. DRAFT

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The likelihood decoder: Error exponents and mismatch

Cited by 23 publications

References 23 publications

Information-Theoretic Foundations of Mismatched Decoding

Information-Theoretic Foundations of Mismatched Decoding

Ensemble Performance of Biometric Authentication Systems Based on Secret Key Generation

Sharp Bounds for Mutual Covering

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