An upper bound for codes in a two-access binary erasure channel (Corresp.)

Tilborg, H. van

doi:10.1109/tit.1978.1055814

Cited by 31 publications

(15 citation statements)

References 3 publications

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“…Our goal is to find necessary conditions for a pair (R 1 , R 2 ) to be admissible. The set of all admissible (R 1 , R 2 ) has been extensively studied in the information theory literature; it is often referred to as the zero-error capacity region of the binary adder channel [1,2,3,4,5,6,7,8,9,10].…”

mentioning

confidence: 99%

An Upper Bound on the Sizes of Multiset-Union-Free Families

Ordentlich

Shayevitz

2016

SIAM J. Discrete Math.

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mentioning

confidence: 99%

An Upper Bound on the Sizes of Multiset-Union-Free Families

Ordentlich

Shayevitz

2016

SIAM J. Discrete Math.

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“…Let us stress here that the complete proof of the smoothness property proof is quite similar to [6,Proposition 4.4], which in turn was inspired by previous work on bounding sizes of Uniquely Decodable Code Pairs (e.g. [35]). However, our presentation will be entirely self-contained.…”

Section: Subset Sum Knapsack and Binary Linear Programmingmentioning

confidence: 99%

Faster Space-Efficient Algorithms for Subset Sum, $k$-Sum, and Related Problems

et al. 2018

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We present randomized algorithms that solve Subset Sum and Knapsack instances with n items in O * (2 0.86n ) time, where the O * (·) notation suppresses factors polynomial in the input size, and polynomial space, assuming random read-only access to exponentially many random bits. These results can be extended to solve Binary Linear Programming on n variables with few constraints in a similar running time. We also show that for any constant k ≥ 2, random instances of k-Sum can be solved using O(n k−0.5 polylog(n)) time and O(log n) space, without the assumption of random access to random bits.Underlying these results is an algorithm that determines whether two given lists of length n with integers bounded by a polynomial in n share a common value. Assuming random read-only access to random bits, we show that this problem can be solved using O(log n) space significantly faster than the trivial O(n 2 ) time algorithm if no value occurs too often in the same list.

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“…Lemma 1 (van Tilborg [12]). Let A, B ⊆ {0, 1} n be a UDCP and let x e , with probability 1+ρ 2 , 1 − x e , with probability 1−ρ 2 .…”

Section: 3mentioning

confidence: 99%

“…Considering upper bounds, the rather direct α + β ≤ 1.5 has been independently found by at least Liao [9], Ahlswede [10], Lindström [11] and van Tilborg [12]. Leaving a gap to the lower bound, 1.5 is still the best upper bound known on α + β in general.…”

Section: Introductionmentioning

confidence: 97%

“…However, Urbanke and Li [6] managed to break through the 1.5 bound in the unbalanced case: assuming α ≥ 1 − for a sufficiently small value of , they showed that β ≤ 0.4921. On a high level, their approach works as follows: a result of van Tilborg [12] (see Lemma 1 below) shows there are not many pairs (a, b) ∈ A×B of small Hamming distance, and if A and B are sufficiently large, then the number of such pairs is bounded from below by an isoperimetric inequality for which the authors use Harper's theorem. Later, this result was improved to β ≤ 0.4798 by Ordentlich and Shayevitz [13].…”

Section: Introductionmentioning

confidence: 99%

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