Related papers: Error Free Perfect Secrecy Systems
Shannon entropy is often a quantity of interest to linguists studying the communicative capacity of human language. However, entropy must typically be estimated from observed data because researchers do not have access to the underlying…
The max-relative entropy together with its smoothed version is a basic tool in quantum information theory. In this paper, we derive the exact exponent for the asymptotic decay of the small modification of the quantum state in smoothing the…
We present information-theoretic definitions and results for analyzing symmetric-key encryption schemes beyond the perfect secrecy regime, i.e. when perfect secrecy is not attained. We adopt two lines of analysis, one based on lossless…
We explore the relation between entanglement entropy of quantum many body systems and the distribution of corresponding, properly selected, observables. Such a relation is necessary to actually measure the entanglement entropy. We show that…
We present a new information-theoretic definition and associated results, based on list decoding in a source coding setting. We begin by presenting list-source codes, which naturally map a key length (entropy) to list size. We then show…
The Shannon lower bound is one of the few lower bounds on the rate-distortion function that holds for a large class of sources. In this paper, it is demonstrated that its gap to the rate-distortion function vanishes as the allowed…
From the output produced by a memoryless deletion channel from a uniformly random input of known length $n$, one obtains a posterior distribution on the channel input. The difference between the Shannon entropy of this distribution and that…
Using the concept of discrete noiseless channels, it was shown by Shannon in A Mathematical Theory of Communication that the ultimate performance of an encoder for a constrained system is limited by the combinatorial capacity of the system…
A common countermeasure against side-channel attacks on secret key cryptographic implementations is $d$th-order masking, which splits each sensitive variable into $d+1$ random shares. In this paper, maximal leakage bounds on the probability…
Privacy is an individual choice to determine which personal details can be collected, used and shared. Individual consent and transparency are the core tenets for earning customers trust and this motivates the organizations to adopt privacy…
We revisit the well-studied problem of estimating the Shannon entropy of a probability distribution, now given access to a probability-revealing conditional sampling oracle. In this model, the oracle takes as input the representation of a…
We consider the lossless compression bound of any individual data sequence. If we fit the data by a parametric model, the entropy quantity $nH({\hat \theta}_n)$ obtained by plugging in the maximum likelihood estimate is an underestimate of…
The classical problem of maximizing the Shannon entropy of a sum of independent random variables supported on a finite alphabet is considered and settled in the ternary case. Namely, the following theorem is established: if…
This paper establishes several converse bounds on the private transmission capabilities of a quantum channel. The main conceptual development builds firmly on the notion of a private state, which is a powerful, uniquely quantum method for…
Shannon entropy is the shortest average codeword length a lossless compressor can achieve by encoding i.i.d. symbols. However, there are cases in which the objective is to minimize the \textit{exponential} average codeword length, i.e. when…
We introduce a new protocol for a lossy data compression algorithm which is based on constraint satisfaction gates. We show that the theoretical capacity of algorithms built from standard parity-check gates converges exponentially fast to…
In order to provide a guaranteed precision and a more accurate judgement about the true value of the Cram\'{e}r-Rao bound and its scaling behavior, an upper bound (equivalently a lower bound on the quantum Fisher information) for precision…
Secure distributed data compression in the presence of an eavesdropper is explored. Two correlated sources that need to be reliably transmitted to a legitimate receiver are available at separate encoders. Noise-free, limited rate links from…
We derive a lower bound on the secrecy capacity of the compound wiretap channel with channel state information at the transmitter which matches the general upper bound on the secrecy capacity of general compound wiretap channels given by…
This paper derives upper and lower bounds on the secrecy capacity-memory tradeoff of a wiretap erasure broadcast channel (BC) with Kw weak receivers and Ks strong receivers, where weak receivers, respectively strong receivers, have same…