On the capacity and codes for the Z-channel

Tallini, Luca G.; Al-Bassam, S.; Böse, B.

doi:10.1109/isit.2002.1023694

Cited by 29 publications

(17 citation statements)

References 1 publication

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“…As ρ → 0, we have θ (RZ) crit → 1, and so for any fixed θ the final case in (28) does not apply in this limit. Furthermore, as ρ → 0, (19) gives − log ρ κ(θ) → 1−θ θ , and we recover the noiseless results (5)- (6). In the appendices, we provide two further claims pertaining to converse results under RZ noise:…”

supporting

confidence: 82%

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Noisy Non-Adaptive Group Testing: A (Near-)Definite Defectives Approach

Scarlett

Johnson

2020

IEEE Trans. Inform. Theory

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The group testing problem consists of determining a small set of defective items from a larger set of items based on a number of possibly-noisy tests, and is relevant in applications such as medical testing, communication protocols, pattern matching, and many more. We study the noisy version of the problem, where the output of each standard noiseless group test is subject to independent noise, corresponding to passing the noiseless result through a binary channel. We introduce a class of algorithms that we refer to as Near-Definite Defectives (NDD), and study bounds on the required number of tests for vanishing error probability under Bernoulli random test designs. In addition, we study algorithm-independent converse results, giving lower bounds on the required number of tests under Bernoulli test designs. Under reverse Z-channel noise, the achievable rates and converse results match in a broad range of sparsity regimes, and under Z-channel noise, the two match in a narrower range of dense/low-noise regimes. We observe that although these two channels have the same Shannon capacity when viewed as a communication channel, they can behave quite differently when it comes to group testing. Finally, we extend our analysis of these noise models to the symmetric noise model, and show improvements over the best known existing bounds in broad scaling regimes.

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confidence: 82%

“…When considered to define a standard noisy communication channel, both the Z-channel and reverse Z-channel have Shannon capacity (in bits/use) given by [19] C Z (ρ) = log 2…”

Section: B Noisy Group Testingmentioning

confidence: 99%

Noisy Non-Adaptive Group Testing: A (Near-)Definite Defectives Approach

Scarlett

Johnson

2020

IEEE Trans. Inform. Theory

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“…We recognize this expression as the capacity of the Z -channel [46], for which the capacity is known to be approx- c and solving for p (for large c), we obtain the given expressions for p and I ( p).…”

Section: Proposition 14mentioning

confidence: 99%

Asymptotics of Fingerprinting and Group Testing: Tight Bounds From Channel Capacities

Laarhoven

2015

IEEE Trans.Inform.Forensic Secur.

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In this paper, we consider the large-coalition asymptotics of various fingerprinting and group testing games, and derive explicit expressions for the capacities for each of these models. We do this both for simple (fast but suboptimal) and arbitrary, joint decoders (slow but optimal). For fingerprinting, we show that if the pirate strategy is known, the capacity often decreases linearly with the number of colluders, instead of quadratically as in the uninformed fingerprinting game. For all considered attacks, the joint capacity is shown to be strictly higher than the simple capacity, including the interleaving attack. This last result contradicts the results of Huang and Moulin regarding the joint fingerprinting capacity, which implies that finding the fingerprinting capacity without restrictions on the tracer's capabilities remains an open problem. For group testing, we improve upon the previous work about the joint capacities, and derive new explicit asymptotics for the simple capacities of various models. These show that the existing simple group testing algorithms of Chan et al. are suboptimal, and that simple decoders cannot asymptotically be as efficient as joint decoders. For the traditional group testing model, we show that the gap between the simple and joint capacities is a factor log 2 (e) ≈ 1.44 for large numbers of defectives.

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“…Whenever On-Off Keying (OOK) modulation is used (see Section 2.4), the sound media can be modeled as a Z-channel [17], i.e., a binary asymmetric channel in which the probability of erroneously decoding a transmitted 1 as a 0 is nil. This fact allows correcting errors using Bloom filters [18].…”

Section: Asymmetric Error Correctionmentioning

confidence: 99%

Encrypted CDMA Audio Network

Ortega¹,

Bettachini²,

Fierens³

et al. 2014

JIS

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We present a secure LAN using sound as the physical layer for low speed applications. In particular, we show a real implementation of a point-to-point or point-to-multipoint secure acoustic network, having a short range, consuming a negligible amount of power, and requiring no specific hardware on mobile clients. The present acoustic network provides VPN-like private channels to multiple users sharing the same medium. It is based on Time-hopping CDMA, and makes use of an encrypted Bloom filter. An asymmetrical error-correction is used to supply data integrity, even in the presence of strong interference. Simulations and real experiments show its feasibility. We also provide some theoretical analysis on the principle of operation.

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On the capacity and codes for the Z-channel

Cited by 29 publications

References 1 publication

Noisy Non-Adaptive Group Testing: A (Near-)Definite Defectives Approach

Noisy Non-Adaptive Group Testing: A (Near-)Definite Defectives Approach

Asymptotics of Fingerprinting and Group Testing: Tight Bounds From Channel Capacities

Encrypted CDMA Audio Network

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