Error Exponent for Multiple Access Channels: Upper Bounds

Nazari, Ali; Pradhan, Sean; Anastasopoulos, Achilleas

doi:10.1109/tit.2015.2424959

Cited by 7 publications

(11 citation statements)

References 17 publications

(10 reference statements)

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“…Remark 2. For convenience, the two parts of the sync sequence y(0) in (10) will be regarded as a single virtual block y (0)y (0) = y(0) as if the decoding window were circular. Instances of some notations will formally refer to the 0'th or K'th block of the sequence (10), these will be interpreted to mean the virtual block.…”

Section: A Notationmentioning

confidence: 99%

“…The decoder employed in this paper will be specified later in Definition 3. Until then the decoder can be any mapping φ (depending on the delay D) that assigns estimates x( î),y( ĵ) of the two input sequences to output sequences z ∈ Z nK , or, equivalently, estimates φ(z) = ( î, ĵ) of i, j in ( 9), (10) (satisfying the condition that îl = 0 and ĵK = 0).…”

Section: A Notationmentioning

confidence: 99%

“…For input sequences ( 9), (10) or equivalently for given i, j, and for output sequence z ∈ Z nK , errorneous decoding means that φ(z) = ( î, ĵ) is not equal to (i, j). As there are 2 n(K−1)(R1+R2) possible choices of (i, j), the average probability of error is…”

Section: A Notationmentioning

confidence: 99%

“…achievable error exponents, have been derived by several authors, see Nazari et al [8] and references there. Upper bounds were given by Harotounian [9] and improved by Nazari et al [10].…”

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confidence: 99%

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Error Exponents for Asynchronous Multiple Access Channels. Controlled Asynchronism may Outperform Synchronism

Farkas¹,

Kói²

2019

Preprint

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Exponential error bounds are derived for frame-asynchronous discrete memoryless multiple access channels with two senders. By numerical evaluation for a particular case, it follows that the reliability function for synchronous transmission may be beaten if the senders are allowed to transmit with an approriately chosen delay. Index Termserror exponents, frame asynchronous channels, multiple-access channels, universal coding, codeword shifting I. INTRODUCTIONDiscrete memoryless multiple access channels (MACs) with two senders will be referred to as synchronous MAC (SMAC) or asynchronous MAC (AMAC) according to the senders' codeword transmissions are frame-synchronous or not. Symbol synchronism is always assumed, its absence could be addressed only in a continuous time model beyond the scope of this paper, see Verdú [1]. The capacity region for SMAC has been determined by Ahlswede[2], and for AMAC with arbitrary unknown delay by Poltyrev [3] and Hui and Humblet [4]. Gaps in [3], [4] were filled in the book of El Gamal and Kim [5] and independently in Farkas and Kói [6]. The capacity region in the asynchronous resp. synchronous case is equal to the union for all P X , P Y of the pentagons R(P X , P Y , W ) defined in ( 5), where W is the channel matrix, respectively the convex closure of the union. The union of these pentagons is non-convex for some choices of W (see, [7]), thus the capacity region of SMAC may be larger than that of AMAC.The error probability of good codes of block-length n, with rate pair inside the capacity region, goes to 0 exponentially as n → ∞. The best possible exponent, called reliability function (as a function of the rate pair) is This paper has been presented in part

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Section: A Notationmentioning

confidence: 99%

Section: A Notationmentioning

confidence: 99%

Section: A Notationmentioning

confidence: 99%

“…achievable error exponents, have been derived by several authors, see Nazari et al [8] and references there. Upper bounds were given by Harotounian [9] and improved by Nazari et al [10].…”

mentioning

confidence: 99%

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Error Exponents for Asynchronous Multiple Access Channels. Controlled Asynchronism may Outperform Synchronism

Farkas¹,

Kói²

2019

Preprint

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“…By considering separate source-channel coding, lower and upper bounds for the error exponent of the MAC were respectively obtained in refs. [ 17 , 18 ]. For the MAC with independent sources, the idea of exploting the dependency between messages and codewords was studied in ref.…”

Section: Introductionmentioning

confidence: 99%

Multi-Class Cost-Constrained Random Coding for Correlated Sources over the Multiple-Access Channel

Rezazadeh

Font-Segura

Martinez

et al. 2021

Entropy

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This paper studies a generalized version of multi-class cost-constrained random-coding ensemble with multiple auxiliary costs for the transmission of N correlated sources over an N-user multiple-access channel. For each user, the set of messages is partitioned into classes and codebooks are generated according to a distribution depending on the class index of the source message and under the constraint that the codewords satisfy a set of cost functions. Proper choices of the cost functions recover different coding schemes including message-dependent and message-independent versions of independent and identically distributed, independent conditionally distributed, constant-composition and conditional constant composition ensembles. The transmissibility region of the scheme is related to the Cover-El Gamal-Salehi region. A related family of correlated-source Gallager source exponent functions is also studied. The achievable exponents are compared for correlated and independent sources, both numerically and analytically.

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On the Reliability Function of Distributed Hypothesis Testing Under Optimal Detection

Weinberger

Kochman

2018

2018 IEEE International Symposium on Information Theory (ISIT)

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The distributed hypothesis testing problem with full side-information is studied. The trade-off (reliability function) between the two types of error exponents under limited rate is studied in the following way. First, the problem is reduced to the problem of determining the reliability function of channel codes designed for detection (in analogy to a similar result which connects the reliability function of distributed lossless compression and ordinary channel codes). Second, a single-letter random-coding bound based on a hierarchical ensemble, as well as a single-letter expurgated bound, are derived for the reliability of channel-detection codes. Both bounds are derived for a system which employs the optimal detection rule. We conjecture that the resulting random-coding bound is ensemble-tight, and consequently optimal within the class of quantization-and-binning schemes. Index TermsBinning, channel-detection codes, distributed hypothesis testing, error exponents, expurgated bounds, hierarchical ensembles, multiterminal data compression, random coding, side information, statistical inference, superposition codes. 2 results from [4], [5] to fully characterize Stein's exponent in the testing against independence case (i.e., when the null hypothesis states that (X, Y ) ∼ P XY , whereas the alternative hypothesis states that (X, Y ) ∼ P X × P Y ).Further, they have used quantization-based encoding to derive an achievable Stein's exponent for a general pair of memoryless hypotheses [2, Th. 5], but without a converse bound. Consecutive progress on this problem, as well as on the symmetric case (in which the Y -observations must also be compressed) is summarized in [27, Sec. IV], with notable contributions from [26], [28], [49]. The the zero-rate case was also considered, for which [26], [28], [48] and [27, Th. 5.5] derived matching achievable and converse bounds under various kind of assumptions on the distributions induced each of the hypotheses. In the last decade, a renewed interest in the problem arose, aimed both at tackling more elaborate models, as well as at improving the results on the basic model. As for the former, notable examples include the following. Stein's exponents under positive rates were explored in successive refinement models [56], for multiple encoders [43], for interactive models [31], [67], under privacy constraints [38], combined with lossy compression [33], over noisy channels [54], [58], for multiple decision centers [46], as well as over multi-hop networks [47]. Exponents for the zero-rate problem were studied under restricted detector structure [41] and for multiple encoders [68]. The finite blocklength and second-order regimes were addressed in [61].Notwithstanding the foregoing progress, the encoding approach proposed in [49] is still the best known in general for the basic model we study in this paper. It is based on quantization and binning, just as used, e.g., for distributed lossy compression (the Wyner-Ziv problem [22, Ch. 11] [66]). First, the encoding rate is reduced by quanti...

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Error Exponent for Multiple Access Channels: Upper Bounds

Cited by 7 publications

References 17 publications

Error Exponents for Asynchronous Multiple Access Channels. Controlled Asynchronism may Outperform Synchronism

Error Exponents for Asynchronous Multiple Access Channels. Controlled Asynchronism may Outperform Synchronism

Multi-Class Cost-Constrained Random Coding for Correlated Sources over the Multiple-Access Channel

On the Reliability Function of Distributed Hypothesis Testing Under Optimal Detection

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