Related papers: Guessing with a Bit of Help
Two estimates for the inverse binary entropy function are derived using the property of information entropy to estimate combinatorics of sequences as well as related formulas from population genetics for the effective number of alleles. The…
Recently published methods enable training of bitwise neural networks which allow reduced representation of down to a single bit per weight. We present a method that exploits ensemble decisions based on multiple stochastically sampled…
We study the setting in which the bits of an unknown infinite binary sequence x are revealed sequentially to an observer. We show that very limited assumptions about x allow one to make successful predictions about unseen bits of x. First,…
Distributional reinforcement learning improves performance by capturing environmental stochasticity, but a comprehensive theoretical understanding of its effectiveness remains elusive. In addition, the intractable element of the infinite…
Quantum resources may provide advantage over their classical counterparts. We say this as quantum advantage. Here we consider a single communication task to study different approaches of observing quantum advantage. We say this setting as a…
Tight lower and upper bounds on the ratio of relative entropies of two probability distributions with respect to a common third one are established, where the three distributions are collinear in the standard $(n-1)$-simplex. These bounds…
We consider the transmission of nonexponentially many messages through a binary symmetric channel with noiseless feedback. We obtain an upper bound for the best decoding error exponent. Combined with the corresponding known lower bound,…
Suppose Alice wishes to send messages to Bob through a communication channel C_1, but her transmissions also reach an eavesdropper Eve through another channel C_2. The goal is to design a coding scheme that makes it possible for Alice to…
This paper explores the two-user Gaussian interference channel through the lens of a natural deterministic channel model. The main result is that the deterministic channel uniformly approximates the Gaussian channel, the capacity regions…
For the information transmission a binary symmetric channel is used. There is also another noisy binary symmetric channel (feedback channel), and the transmitter observes without delay all the outputs of the forward channel via that…
We study optimal rates for quantum communication over a single use of a channel, which itself can correspond to a finite number of uses of a channel with arbitrarily correlated noise. The corresponding capacity is often referred to as the…
In query learning, the goal is to identify an unknown object while minimizing the number of "yes" or "no" questions (queries) posed about that object. A well-studied algorithm for query learning is known as generalized binary search (GBS).…
This paper is on developing some computer-assisted proof methods involving non-classical inequalities for Shannon entropy. Two areas of the applications of information inequalities are studied: Secret sharing schemes and hat guessing games.…
For two-user interference channels, the capacity is known for the case where interference is stronger than the desired signal. Moreover, it is known that if the interference is above a certain level, it does not reduce the capacity at all.…
The brain interprets ambiguous sensory information faster and more reliably than modern computers, using neurons that are slower and less reliable than logic gates. But Bayesian inference, which underpins many computational models of…
Recent work has established that when transmitter Alice wishes to communicate reliably to recipient Bob without detection by warden Willie, with additive white Gaussian noise (AWGN) channels between all parties, communication is limited to…
We consider a new formulation of a class of synchronization error channels and derive analytical bounds and numerical estimates for the capacity of these channels. For the binary channel with only deletions, we obtain an expression for the…
Suppose that $Y^n$ is obtained by observing a uniform Bernoulli random vector $X^n$ through a binary symmetric channel with crossover probability $\alpha$. The "most informative Boolean function" conjecture postulates that the maximal…
We consider a standard two-source model for uniform common randomness (UCR) generation, in which Alice and Bob observe independent and identically distributed (i.i.d.) samples of a correlated finite source and where Alice is allowed to send…
Suppose Alice wishes to send messages to Bob through a communication channel C_1, but her transmissions also reach an eavesdropper Eve through another channel C_2. The goal is to design a coding scheme that makes it possible for Alice to…