A Combinatory Detection Problem

Söderberg, Staffan; Shapiro, H. S.

doi:10.1080/00029890.1963.11992174

Cited by 103 publications

(23 citation statements)

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“…This problem was studied by Cantor in [8], Soderberg and Shapiro in [35] Erdös and Rényi in [18], Lindström in [26][27][28][29] and Cantor and Mills in [10]. Lindström [26] and independently Cantor and Mills [10] gave a non-adaptive polynomial time algorithm for the problem with query complexity that matches the lower bound.…”

Section: Introductionmentioning

confidence: 85%

On the Coin Weighing Problem with the Presence of Noise

Bshouty

2012

Lecture Notes in Computer Science

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Abstract. In this paper we consider the following coin weighing problem: Given n coins for which some of them are counterfeit with the same weight. The problem is: given the weights of the counterfeit coin and the authentic coin, detect the counterfeit coins a with minimal number of weighings. This problem has many applications in computational learning theory, compressed sensing and multiple access adder channels.An old optimal non-adaptive polynomial time algorithm of Lindstrom can detect the counterfeit coins with O(n/ log n) weighings. An information theoretic proof shows that Lindstrom's algorithm is optimal. In this paper we study non-adaptive algorithms for this problem when some of the answers of the weighings received are incorrect or unknown.We show that no coin weighing algorithm exists that can detect the counterfeit coins when the number of incorrect weighings is more than 1/4 fraction of the number of weighings. We also give the tight bound Θ(n/ log n) for the number of weighings when the number of incorrect answers is less than 1/4 fraction of the number of weighings.We then give a non-adaptive polynomial time algorithm that detects the counterfeit coins with k = O(n/ log log n) weighings even if some constant fraction of the answers of the weighings received are incorrect. This improves Bshouty and Mazzawi's algorithm [7] that uses O(n) weighings. This is the first sublinear algorithm for this problem.

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Section: Introductionmentioning

confidence: 85%

On the Coin Weighing Problem with the Presence of Noise

Bshouty

2012

Lecture Notes in Computer Science

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“…Finding those overloaded UD class of codes for noiseless channel is directly related to coin-weighing problem, one of Erdös' problems in [18]. It is a special case of a general problem and in literature [19] - [22] authors used the term detecting matrices. Lindström in [23] defines the same problem as the detecting set of vectors.…”

Section: Introductionmentioning

confidence: 99%

“…The choice of coins for a weighing must not depend on results of previous weighings. This problem was first introduced by H. S. Shapiro [19] for n = 5. Only few cases of n was proved the minimal number of L, however for larger n the f 2 (n) has been estimated [24].…”

Section: Introductionmentioning

confidence: 99%

Fast Decoder for Overloaded Uniquely Decodable Synchronous Optical CDMA

Kulhandjian

D’Amours

et al. 2019

2019 IEEE Wireless Communications and Networking Conference (WCNC)

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In this paper, we propose a fast decoder algorithm for uniquely decodable (errorless) code sets for overloaded synchronous optical code-division multiple-access (O-CDMA) systems. The proposed decoder is designed in a such a way that the users can uniquely recover the information bits with a very simple decoder, which uses only a few comparisons. Compared to maximum-likelihood (ML) decoder, which has a high computational complexity for even moderate code lengths, the proposed decoder has much lower computational complexity. Simulation results in terms of bit error rate (BER) demonstrate that the performance of the proposed decoder for a given BER requires only 1 − 2 dB higher signal-to-noise ratio (SNR) than the ML decoder.

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“…The uniquely decodable coding methods for overloaded synchronous code-division multiple-access (CDMA) where the number of multiplexed signals K is greater than the spreading gain or code (signature) length L has been studied in [1]- [15]. An overloaded code set C of dimension L × K is considered to be "errorless", or uniquely decodable (UD) in a noiseless multiplexed transmission if for all possible K × 1 vectors x 1 and x 2 , where x 1 = x 2 ∈ {±1} K×1 and Cx 1 = Cx 2 [2].…”

Section: Introductionmentioning

confidence: 99%

Uniquely Decodable Ternary Codes for Synchronous CDMA Systems

Kulhandjian

D’Amours

Kulhandjian

2018

2018 IEEE 29th Annual International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC)

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In this paper, we consider the problem of recursively designing uniquely decodable ternary code sets for highly overloaded synchronous code-division multipleaccess (CDMA) systems. The proposed code set achieves larger number of users K < K t max than any other known state-of-the-art ternary codes that offer low-complexity decoders in the noisy transmission. Moreover, we propose a simple decoder that uses only a few comparisons and can allow the user to uniquely recover the information bits. Compared to maximum likelihood (ML) decoder, which has a high computational complexity for even moderate code length, the proposed decoder has much lower computational complexity. We also derived the computational complexity of the proposed recursive decoder analytically. Simulation results show that the performance of the proposed decoder is almost as good as the ML decoder. * where γ(n) function is the number of ones in the binary expansion of all positive integers less than n.

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A Combinatory Detection Problem

Cited by 103 publications

References 0 publications

On the Coin Weighing Problem with the Presence of Noise

On the Coin Weighing Problem with the Presence of Noise

Fast Decoder for Overloaded Uniquely Decodable Synchronous Optical CDMA

Uniquely Decodable Ternary Codes for Synchronous CDMA Systems

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