Bounds on conditional probabilities with applications in multi-user communication

Ahlswede, Rudolf; Gács, Péter; Körner, János

doi:10.1007/bf00535682

Cited by 141 publications

(190 citation statements)

References 7 publications

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“…In order to use Lemma 2 for proving Theorem 1, an important step involves controlling the size of X in Lemma 2. To this end, we use the following scalar quantizer to quantize the alphabet X i (in (13)) which is exponential in the blocklength n (cf. (14)) so that its quantized version is an alphabet whose size is polynomial in the blocklength.…”

Section: B Wringing Techniquementioning

confidence: 99%

A proof of the strong converse theorem for Gaussian multiple access channels

Fong

Tan

2015

2015 IEEE Information Theory Workshop - Fall (ITW)

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We prove the strong converse for the N -source Gaussian multiple access channel (MAC). In particular, we show that any rate tuple that can be supported by a sequence of codes with asymptotic average error probability less than one must lie in the Cover-Wyner capacity region. Our proof consists of the following. First, we perform an expurgation step to convert any given sequence of codes with asymptotic average error probability less than one to codes with asymptotic maximal error probability less than one. Second, we quantize the input alphabets with an appropriately chosen resolution. Upon quantization, we apply the wringing technique (by Ahlswede) on the quantized inputs to obtain further subcodes from the subcodes obtained in the expurgation step so that the resultant correlations among the symbols transmitted by the different sources vanish as the blocklength grows. Finally, we derive upper bounds on achievable sum-rates of the subcodes in terms of the type-II error of a binary hypothesis test. These upper bounds are then simplified through judicious choices of auxiliary output distributions. Our strong converse result carries over to the Gaussian interference channel under strong interference as long as the sum of the two asymptotic average error probabilities less than one.

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Section: B Wringing Techniquementioning

confidence: 99%

A proof of the strong converse theorem for Gaussian multiple access channels

Fong

Tan

2015

2015 IEEE Information Theory Workshop - Fall (ITW)

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“…A closely related result was discovered in [3] and rediscovered in [5]: For a given number u C [0,2 n] of arbitrary subsets of an n-set the "Hamming distance 1"-boundary is minimal for the initial segment of size u, also called in short "u-th initial segment", in the H-order (of [3]), that is, if one chooses all subsets of cardinality less than n-k (k suitable) and all remaining subsets of cardinality n-k, whose complements are in the initial segment of the squashed order.…”

Section: Introduction and Resultsmentioning

confidence: 61%

“…A prototype of a discrete isoperimetric inequality is the one discovered in [3], rediscovered in [5], and proved again in [6]. Here d equals the Hamming distance dH and is defined on X n • X n.…”

Section: Two Isoperimetric Inequalitiesmentioning

confidence: 99%

Shadows and isoperimetry under the sequence-subsequence relation

Ahlswede

Cai

1997

Combinatorica

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“…A new and general method to prove strong converses was presented in [7]. It applies to many multi-user coding problems for which all classical approaches fail.…”

Section: P(y"]x")= ~ W(ytlx)mentioning

confidence: 99%

“…We need a result of Margulis [8] in the slightly generalized form given in [7] as Lemma 4: n Lemma. Given a DMC with transmission probabilities P=I]w there is a constant c=c(w)>O such that for any n, Bc~" and x"~Y'": 1 …”

Section: Proof Of the Theoremmentioning

confidence: 99%