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 and the eavesdropper, Eve, only one. In one scenario—the “guessing version”—we require that the expected number of guesses it takes Bob to guess the password approach one as$n$tends to infinity, and in the second—the “listsize version”—that the expected size of the shortest list that Bob must form to guarantee that it contain the password approach one. Assuming that Alice cannot control which hint 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 Massey–Arikan guessing, Bunte–Lapidoth task-encoding, and the close relation between them. A generalization that allows for Alice to produce$\delta $(not necessarily two) hints, for Bob to observe$\nu $(not necessarily two) of the hints, and for Eve to observe$\eta $(not necessarily one) of the hints is also discussed. This models scenarios where hints are stored on fail-prone disks.

The zero-error feedback capacity of the Gel'fand-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.

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.

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. An extension to the three-receiver BC is also discussed: an inner bound on the ID capacity region is obtained, and that is shown to be in some cases tight.

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.

We study the secrecy of a distributed-storage system for passwords. The encoder, Alice, observes a length-n password and describes it using δ s-bit hints, which she stores in different locations. The legitimate receiver, Bob, observes ν of those hints. In one scenario we require that the expected number of guesses it takes Bob to guess the password approach 1 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 1. The eavesdropper, Eve, sees η < ν hints. Assuming that Alice cannot control which hints Bob and Eve observe, we characterize for each scenario the largest normalized (by n) exponent that we can guarantee for the expected number of guesses it takes Eve to guess the password.

The capacity of the semideterministic discrete memoryless broadcast channel (SD-BC) with partial message side-information (P-MSI) at the receivers is established. In the setting without a common message, it is shown that P-MSI to the stochastic receiver alone can increase capacity, whereas P-MSI to the deterministic receiver can only increase capacity if also the stochastic receiver has P-MSI. The latter holds only for the setting without a common message: if the encoder also conveys a common message, then P-MSI to the deterministic receiver alone can increase capacity. These capacity results are used to show that feedback from the stochastic receiver can increase the capacity of the SD-BC without P-MSI and the sum-rate capacity of the SD-BC with P-MSI at the deterministic receiver. The link between P-MSI and feedback is a feedback code, which-roughly speaking-turns feedback into P-MSI at the stochastic receiver, and hence helps the stochastic receiver mitigate experienced interference. For the case, where the stochastic receiver has full MSI (F-MSI) and can thus fully mitigate experienced interference also in the absence of feedback, it is shown that feedback cannot increase capacity.

This paper considers the inverse problem with observed variables Y = BGX ⊕ Z, where BGis the incidence matrix of a graph G, X is the vector of unknown vertex variables with a uniform prior, and Z is a noise vector with Bernoulli(ε) i.i.d. entries. All variables and operations are Boolean. This model is motivated by coding, synchronization, and community detection problems. In particular, it corresponds to a stochastic block model or a correlation clustering problem with two communities and censored edges. Without noise, exact recovery of X is possible if and only the graph G is connected, with a sharp threshold at the edge probability log(n)=n for Erdös-Rényi random graphs. The first goal of this paper is to determine how the edge probability p needs to scale to allow exact recovery in the presence of noise. Defining the degree (oversampling) rate of the graph by α = np= log(n), it is shown that exact recovery is possible if and only if α > 2/(1-2ε)2+o(1/(1-2ε)2). In other words, 2/(1-2ε)2is the information theoretic threshold for exact recovery at low-SNR. In addition, an efficient recovery algorithm based on semidefinite programming is proposed and shown to succeed in the threshold regime up to twice the optimal rate. Full version available in [1].

We show that the identification (ID) capacity of the two-receivers broadcast channel is the set of rate pairs satisfying that, for some distribution on the input, each receiver's ID rate does not exceed the mutual information between the input and the output that it observes. The capacity's interior is achieved by codes with deterministic encoders. Our results hold under the average error criterion, which requires that each receiver reliably identify its message if the other receiver's message is uniformly distributed. Key in the proof is a new ID code for the single-user channel.

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. In one scenario we require that the number of guesses it takes Bob to guess the password approach 1 as n tends to infinity and in the other that the size of the list that Bob must form to guarantee that it contain the password approach 1. The eavesdropper, Eve, sees only one of the hints; Alice cannot control which. For each scenario we characterize the largest normalized (by n) exponent that we can guarantee for the number of guesses it takes Eve to guess the password.

The benefits afforded by feedback and/or causal state information (SI) on the state-dependent discrete memoryless multiple-access channel (SD-MAC) with cribbing encoder/s are studied. Capacity regions are derived for communication scenarios whose capacities without cribbing are still unknown. It is shown that when the encoders can crib, the SD-MAC behaves less like a MAC and more like a single-user channel: 1) feedback does not help; 2) strictly causal SI does not help; and 3) causal SI to both encoders is best utilized using Shannon strategies. However, in asymmetric settings, the single-user-like behavior may or may not occur. For example, the SD-MAC with only one cribbing encoder is single-user-like when the state is revealed to the cribbing encoder, but not if it is revealed to the noncribbing encoder.

We consider the recovery of sparse signals subject to sparse interference, as introduced by Studer , IEEE T-IT, 2012. We present novel probabilistic recovery guarantees for this framework, covering varying degrees of knowledge of the signal and interference support, which are relevant for a large number of practical applications. Our results assume that the sparsifying dictionaries are characterized by coherence parameters and we require randomness only in the signal and/or interference. The obtained recovery guarantees show that one can recover sparsely corrupted signals with overwhelming probability, even if the sparsity of both the signal and interference scale (near) linearly with the number of measurements.

We show that the capacity region of the state-dependent multiple-access channel (SD-MAC) with strictly-causally cribbing encoders is not enlarged if strictly-causal state-information (SI) and feedback are furnished to the encoders. We also derive the capacity region of the SD-MAC with causal SI at the cribbing encoders and show that Shannon strategies are optimal. Such strategies are generally suboptimal if the encoders access distinct SI. However, Shannon strategies are optimal and we have a characterization of the capacity region for the case where both encoders crib, causal SI is revealed to one encoder, and feedback is available to the other encoder.

In this paper, we present novel probabilistic recovery guarantees for sparse signals subject to sparse interference, covering varying degrees of knowledge of the signal and interference support. Our results assume that the sparsifying dictionaries are characterized by coherence parameters and we require randomness only in the signal and/or interference. The obtained recovery guarantees show that one can recover sparsely corrupted signals with overwhelming probability, even if the sparsity of both the signal and interference scale (near) linearly with the number of measurements.