Second-Order Rate Region of Constant-Composition Codes for the Multiple-Access Channel

Scarlett, Jonathan; Martínez, Alfonso García; i, Fàbregas, Albert Guillén

doi:10.48550/arxiv.1303.6167

Cited by 2 publications

(5 citation statements)

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“…Other authors [84,111,112,136] also considered inner bounds to the (n, ε)-rate regions (also called global achievability regions) for the discrete memoryless and Gaussian MACs, but it appears that conclusive results are much harder to derive without any further assumptions on the channel model. These are multi-terminal channel coding analogues of the corresponding discussion for Slepian-Wolf coding in Section 6.4.3.…”

Section: Summary and Other Resultsmentioning

confidence: 99%

“…that for lossless source coding in (3.14)), they do not provide the complete picture with regard to the convergence of rate pairs to a fundamental limit, e.g., a corner point of the Slepian-Wolf region. Indeed, an achievability statement similar to (6.53) holds for the DM-MAC for each input distribution [84,111,136,156] and hence the union over all input distributions. However, one of the major deficiencies of such a statement is that the O(log n) third-order term is not uniform in the input distributions; this poses serious challenges in the interpretation of the result if we consider random coding using a sequence of input distributions that varies with the blocklength (cf.…”

Section: Global Approachesmentioning

confidence: 95%

“…In the absence of the degraded message sets (or asymmetry) assumption, one needs to develop a converse technique, possibly related to the wringing technique of Ahlswede [3], to assert that the given codewords pairs are almost independent (or almost orthogonal for the Gaussian case). By leveraging the degraded message sets assumption, we circumvented this requirement in this chapter but for the MAC, it is not clear whether the wringing technique yields a redundancy term that matches the best known inner bound to the second-order region [112,136]. fixed error probability analogue of Forney's analysis of erasure and list decoding from the error exponents perspective [55].…”

Section: Difficulties In the Fixed Error Analysis For The Macmentioning

confidence: 99%

“…This is because there does not exist an analogue of the relation in (4.24), where the unconditional information is equal to the conditional information variance for all CAIDs. Scarlett-Martinez-Guillén i Fàbregas [136] provided the best known inner bounds to the (n, ε)-rate region for the discrete memoryless MAC. Tan-Kosut [157] also showed that conditionally constant composition codes also outperforms i.i.d.…”

Section: Multi-terminal Information Theorymentioning

confidence: 99%

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Asymptotic Estimates in Information Theory with Non-Vanishing Error Probabilities

Tan

2014

FNT in Communications and Information Theory

118

103

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This monograph presents a unified treatment of single-and multi-user problems in Shannon's information theory where we depart from the requirement that the error probability decays asymptotically in the blocklength. Instead, the error probabilities for various problems are bounded above by a non-vanishing constant and the spotlight is shone on achievable coding rates as functions of the growing blocklengths. This represents the study of asymptotic estimates with non-vanishing error probabilities.In Part I, after reviewing the fundamentals of information theory, we discuss Strassen's seminal result for binary hypothesis testing where the type-I error probability is non-vanishing and the rate of decay of the type-II error probability with growing number of independent observations is characterized. In Part II, we use this basic hypothesis testing result to develop second-and sometimes, even third-order asymptotic expansions for point-to-point communication. Finally in Part III, we consider network information theory problems for which the second-order asymptotics are known. These problems include some classes of channels with random state, the multiple-encoder distributed lossless source coding (Slepian-Wolf) problem and special cases of the Gaussian interference and multiple-access channels. Finally, we discuss avenues for further research.

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Section: Summary and Other Resultsmentioning

confidence: 99%

Section: Global Approachesmentioning

confidence: 95%

Section: Difficulties In the Fixed Error Analysis For The Macmentioning

confidence: 99%

Section: Multi-terminal Information Theorymentioning

confidence: 99%

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Asymptotic Estimates in Information Theory with Non-Vanishing Error Probabilities

Tan

2014

FNT in Communications and Information Theory

118

103

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show abstract

“…On the other hand, in Theorem 2, essentially all the average error probability is assigned to the joint outage event and a multi-dimensional CLT is applied. This latter approach, which leads to a relatively larger region, is similar to that in [31]- [33] for the discrete MAC. Finally, we would like to point out that the statements of Theorems 2 and 3 correct a slight error in the corresponding result in our conference version of this work [15], in which the term V 3 (P 1 , P 2 ) defined in (104) was missing in (99) and (105).…”

Section: A System Model and Main Resultsmentioning

confidence: 72%

A Finite-Blocklength Perspective on Gaussian Multi-Access Channels

MolavianJazi,

Laneman

2013

Preprint

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Motivated by the growing application of wireless multi-access networks with stringent delay constraints, we investigate the Gaussian multiple access channel (MAC) in the finite blocklength regime. Building upon information spectrum concepts, we develop several non-asymptotic inner bounds on channel coding rates over the Gaussian MAC with a given finite blocklength, positive average error probability, and maximal power constraints. Employing Central Limit Theorem (CLT) approximations, we also obtain achievable second-order coding rates for the Gaussian MAC based on an explicit expression for its dispersion matrix. We observe that, unlike the pentagon shape of the asymptotic capacity region, the second-order region has a curved shape with no sharp corners.A main emphasis of the paper is to provide a new perspective on the procedure of handling input cost constraints for tight achievability proofs. Contrary to the complicated achievability techniques in the literature, we show that with a proper choice of input distribution, tight bounds can be achieved via the standard random coding argument and a modified typicality decoding. In particular, we prove that codebooks generated randomly according to independent uniform distributions on the respective "power shells" perform far better than both independent and identically distributed (i.i.d.) Gaussian inputs and TDMA with power control. Interestingly, analogous to an error exponent result of Gallager, the resulting achievable region lies roughly halfway between that of the i.i.d. Gaussian inputs and that of a hypothetical "sum-power shell" input. However, dealing with such a non-i.i.d. input requires additional analysis such as a new change of measure technique and application of a Berry-Esseen CLT for functions of random variables.

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Second-Order Rate Region of Constant-Composition Codes for the Multiple-Access Channel

Cited by 2 publications

References 0 publications

Asymptotic Estimates in Information Theory with Non-Vanishing Error Probabilities

Asymptotic Estimates in Information Theory with Non-Vanishing Error Probabilities

A Finite-Blocklength Perspective on Gaussian Multi-Access Channels

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