arXiv subjects

Amos Lapidoth

Publications and source records attributed to Amos Lapidoth.

At least 19 recordsLinked to original sources

arXiv2026

The Equivalence of Causal and Noncausal State Information on Bipartite Networks With State-Cognizant Receivers

State-dependent bipartite networks with state-cognizant receivers and state-informed transmitters are studied. Such networks have no nodes that both transmit and receive. Examples are the multi-access channel, the broadcast channel, and the interference channel. Without computing the capacity region of the network, it is shown that if the state sequence is ergodic and autonomous, and if, conditionally on the state sequence, the network law is memoryless, then the network capacity region does not depend on whether the state information is provided to the encoders causally or noncausally.

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arXiv2024

The State-Dependent Channel with a Rate-Limited Cribbing Helper

The capacity of a memoryless state-dependent channel is derived for a setting in which the encoder is provided with rate-limited assistance from a cribbing helper that observes the state sequence causally and the past channel inputs strictly-causally. Said cribbing may increase capacity but not to the level achievable by a message-cognizant helper.

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arXiv2023

State-Dependent Channels with a Message-Cognizant Helper

The capacity of a state-dependent discrete memoryless channel (SD-DMC) is derived for the setting where a message-cognizant rate-limited helper observes the state sequence noncausally, produces its description, and provides the description to both encoder and decoder.

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arXiv2023

Message-Cognizant Assistance and Feedback for the Gaussian Channel

A formula is derived for the capacity of the Gaussian channel with a benevolent message-cognizant rate-limited helper that provides a noncausal description of the noise to the encoder and decoder. This capacity is strictly larger than when the helper is message oblivious, with the difference being particularly pronounced at low signal-to-noise ratios. It is shown that in this setup, a feedback link from the receiver to the encoder does not increase capacity. However, in the presence of such a link, said capacity can be achieved even if the helper is oblivious to the transmitted message.

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arXiv2023

State-Dependent DMC with a Causal Helper

A memoryless state sequence governing the behavior of a memoryless state-dependent channel is to be described causally to an encoder wishing to communicate over said channel. Given the maximal-allowed description rate, we seek the description that maximizes the Shannon capacity. It is shown that the maximum need not be achieved by a memoryless (symbol-by-symbol) description. Such descriptions are, however, optimal when the receiver is cognizant of the state sequence or when the description is allowed to depend on the message. For other cases, a block-Markov scheme with backward decoding is proposed.

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arXiv2021

Guessing Based on Compressed Side Information

A source sequence is to be guessed with some fidelity based on a rate-limited description of an observed sequence with which it is correlated. The trade-off between the description rate and the exponential growth rate of the least power mean of the number of guesses is characterized.

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arXiv2019

Two Measures of Dependence

Two families of dependence measures between random variables are introduced. They are based on the Rényi divergence of order $α$ and the relative $α$-entropy, respectively, and both dependence measures reduce to Shannon's mutual information when their order $α$ is one. The first measure shares many properties with the mutual information, including the data-processing inequality, and can be related to the optimal error exponents in composite hypothesis testing. The second measure does not satisfy the data-processing inequality, but appears naturally in the context of distributed task encoding.

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arXiv2019

Gambling and Rényi Divergence

For gambling on horses, a one-parameter family of utility functions is proposed, which contains Kelly's logarithmic criterion and the expected-return criterion as special cases. The strategies that maximize the utility function are derived, and the connection to the Rényi divergence is shown. Optimal strategies are also derived when the gambler has some side information; this setting leads to a novel conditional Rényi divergence.

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arXiv2018

Testing Against Independence and a Rényi Information Measure

The achievable error-exponent pairs for the type I and type II errors are characterized in a hypothesis testing setup where the observation consists of independent and identically distributed samples from either a known joint probability distribution or an unknown product distribution. The empirical mutual information test, the Hoeffding test, and the generalized likelihood-ratio test are all shown to be asymptotically optimal. An expression based on a Renyi measure of dependence is shown to be the Fenchel biconjugate of the error-exponent function obtained by fixing one error exponent and optimizing the other. An example is provided where the error-exponent function is not convex and thus not equal to its Fenchel biconjugate.

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arXiv2017

Semi-Robust Communications over a Broadcast Channel

We establish the deterministic-code capacity region of a network with one transmitter and two receivers: an "ordinary receiver" and a "robust receiver." The channel to the ordinary receiver is a given (known) discrete memoryless channel (DMC), whereas the channel to the robust receiver is an arbitrarily varying channel (AVC). Both receivers are required to decode the "common message," whereas only the ordinary receiver is required to decode the "private message."

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arXiv2017

Identification via the Broadcast Channel

The identification (ID) capacity region of the two-receiver broadcast channel (BC) is shown to be the set of rate-pairs for which, for some distribution on the channel input, each receiver's ID rate does not exceed the mutual information between the channel input and the channel output that it observes. Moreover, the capacity region's interior is achieved by codes with deterministic encoders. The results are obtained under the average-error criterion, which requires that each receiver reliably identify its message whenever the message intended for the other receiver is drawn at random. They hold also for channels whose transmission capacity region is to-date unknown. Key to the proof is a new ID code construction for the single-user channel. Extensions to the BC with one-sided feedback and the three-receiver BC are also discussed: inner bounds on their ID capacity regions are obtained, and those are shown to be in some cases tight.

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arXiv2017

Distributed Task Encoding

The rate region of the task-encoding problem for two correlated sources is characterized using a novel parametric family of dependence measures. The converse uses a new expression for the $ρ$-th moment of the list size, which is derived using the relative $α$-entropy.

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arXiv2017

Guessing Attacks on Distributed-Storage Systems

The secrecy of a distributed-storage system for passwords is studied. The encoder, Alice, observes a length-n password and describes it using two hints, which she stores in different locations. The legitimate receiver, Bob, observes both hints. In one scenario the requirement is that the expected number of guesses it takes Bob to guess the password approach one as n tends to infinity, and in the other that the expected size of the shortest list that Bob must form to guarantee that it contain the password approach one. The eavesdropper, Eve, sees only one of the hints. Assuming that Alice cannot control which hints Eve observes, the largest normalized (by n) exponent that can be guaranteed for the expected number of guesses it takes Eve to guess the password is characterized for each scenario. Key to the proof are new results on Arikan's guessing and Bunte and Lapidoth's task-encoding problem; in particular, the paper establishes a close relation between the two problems. A rate-distortion version of the model is also discussed, as is a generalization that allows for Alice to produce δ (not necessarily two) hints, for Bob to observe ν (not necessarily two) of the hints, and for Eve to observe η (not necessarily one) of the hints. The generalized model is robust against δ - ν disk failures.

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arXiv2016

The Zero-Error Feedback Capacity of State-Dependent Channels

The zero-error feedback capacity of the Gelfand-Pinsker channel is established. It can be positive even if the channel's zero-error capacity is zero in the absence of feedback. Moreover, the error-free transmission of a single bit may require more than one channel use. These phenomena do not occur when the state is revealed to the transmitter causally, a case that is solved here using Shannon strategies. Cost constraints on the channel inputs or channel states are also discussed, as is the scenario where---in addition to the message---also the state sequence must be recovered.

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arXiv2015

Maximum Rényi Entropy Rate

Two maximization problems of Rényi entropy rate are investigated: the maximization over all stochastic processes whose marginals satisfy a linear constraint, and the Burg-like maximization over all stochastic processes whose autocovariance function begins with some given values. The solutions are related to the solutions to the analogous maximization problems of Shannon entropy rate.

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arXiv2014

On the Listsize Capacity with Feedback

The listsize capacity of a discrete memoryless channel is the largest transmission rate for which the expectation---or, more generally, the $ρ$-th moment---of the number of messages that could have produced the output of the channel approaches one as the blocklength tends to infinity. We show that for channels with feedback this rate is upper-bounded by the maximum of Gallager's $E_0$ function divided by $ρ$, and that equality holds when the zero-error capacity of the channel is positive. To establish this inequality we prove that feedback does not increase the cutoff rate. Relationships to other notions of channel capacity are explored.

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arXiv2014

Encoding Tasks and Rényi Entropy

A task is randomly drawn from a finite set of tasks and is described using a fixed number of bits. All the tasks that share its description must be performed. Upper and lower bounds on the minimum $ρ$-th moment of the number of performed tasks are derived. The case where a sequence of tasks is produced by a source and $n$ tasks are jointly described using $nR$ bits is considered. If $R$ is larger than the Rényi entropy rate of the source of order $1/(1+ρ)$ (provided it exists), then the $ρ$-th moment of the ratio of performed tasks to $n$ can be driven to one as $n$ tends to infinity. If $R$ is smaller than the Rényi entropy rate, this moment tends to infinity. The results are generalized to account for the presence of side-information. In this more general setting, the key quantity is a conditional version of Rényi entropy that was introduced by Arimoto. For IID sources two additional extensions are solved, one of a rate-distortion flavor and the other where different tasks may have different nonnegative costs. Finally, a divergence that was identified by Sundaresan as a mismatch penalty in the Massey-Arikan guessing problem is shown to play a similar role here.

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arXiv2014

Distributed Storage for Data Security

We study the secrecy of a distributed storage system for passwords. The encoder, Alice, observes a length-n password and describes it using two hints, which she then stores in different locations. The legitimate receiver, Bob, observes both hints. The eavesdropper, Eve, sees only one of the hints; Alice cannot control which. We characterize the largest normalized (by n) exponent that we can guarantee for the number of guesses it takes Eve to guess the password subject to the constraint that either the number of guesses it takes Bob to guess the password or the size of the list that Bob must form to guarantee that it contain the password approach 1 as n tends to infinity.

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