Mismatched multi-letter successive decoding for the multiple-access channel

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

doi:10.1109/isit.2014.6875292

Cited by 3 publications

(15 citation statements)

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“…We proceed by characterizing the behavior of the expectation in (24) for the joint types P XY with P X = Q n and P Y = P Y , using properties of type class enumerators. The arguments follow those of [24], [25], and are based on the fact that N y ( P XY ) has a Binomial distribution with exponentially many terms (M −1 . = e nR ) and an exponentially small success probability (P (X, y) ∈ T n ( P XY ) .…”

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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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%

The likelihood decoder: Error exponents and mismatch

Scarlett

Martinez

Fàbregas

2015

2015 IEEE International Symposium on Information Theory (ISIT)

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“…In Chapter 5, we considered maximum-metric decoding for the multiple-access channel (MAC). In [74], a mismatched multi-letter successive decoding rule was instead adopted, with the two decoding steps taking the form m1 = arg max i j q n (x…”

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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“…Although the motivation in [21] is different, the codebook construction and the decoding rule are the same as in the first part of this paper, and thus, essentially, their results apply also for the IFC. It is important to emphasize that while we believe that our error exponent analysis is somewhat simpler, at least conceptually, there is strong resemblance between our analysis and [21], as they both based on type enumeration techniques. Note, however, that while in [21] the standard union bound was used, here, the new upper bounds mentioned above, provide some potential gain over [21], even for the ordinary ensemble.…”

Section: Introductionmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

“…• Recently, in [21,22], the authors independently suggested lower bounds on the error exponents of both standard and cognitive multiple-access channels (MACs), assuming suboptimal successive decoding scheme, and using the standard random coding ensemble (considered in Subsection III-B). Although the motivation in [21] is different, the codebook construction and the decoding rule are the same as in the first part of this paper, and thus, essentially, their results apply also for the IFC. It is important to emphasize that while we believe that our error exponent analysis is somewhat simpler, at least conceptually, there is strong resemblance between our analysis and [21], as they both based on type enumeration techniques.…”

Section: Introductionmentioning

confidence: 99%

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Random Coding Error Exponents for the Two-User Interference Channel

Huleihel

Merhav

2017

IEEE Trans. Inform. Theory

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This paper is about deriving lower bounds on the error exponents for the two-user interference channel under the random coding regime for several ensembles. Specifically, we first analyze the standard random coding ensemble, where the codebooks are comprised of independently and identically distributed (i.i.d.) codewords. For this ensemble, we focus on optimum decoding, which is in contrast to other, suboptimal decoding rules that have been used in the literature (e.g., joint typicality decoding, treating interference as noise, etc.). The fact that the interfering signal is a codeword, rather than an i.i.d. noise process, complicates the application of conventional techniques of performance analysis of the optimum decoder. Also, unfortunately, these conventional techniques result in loose bounds. Using analytical tools rooted in statistical physics, as well as advanced union bounds, we derive single-letter formulas for the random coding error exponents. We compare our results with the best known lower bound on the error exponent, and show that our exponents can be strictly better. Then, in the second part of this paper, we consider more complicated coding ensembles, and find a lower bound on the error exponent associated with the celebrated Han-Kobayashi (HK) random coding ensemble, which is based on superposition coding.

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Mismatched multi-letter successive decoding for the multiple-access channel

Cited by 3 publications

References 13 publications

The likelihood decoder: Error exponents and mismatch

The likelihood decoder: Error exponents and mismatch

Information-Theoretic Foundations of Mismatched Decoding

Random Coding Error Exponents for the Two-User Interference Channel

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