Related papers: Probabilistic analysis of arithmetic coding showin…
We develop efficient binary (i.e., 1-bit) and multi-bit coding schemes for estimating the scale parameter of $\alpha$-stable distributions. The work is motivated by the recent work on one scan 1-bit compressed sensing (sparse signal…
A systematic study of the probability distribution of superimposed random codes is presented through the use of generating functions. Special attention is paid to the cases of either uniformly distributed but not necessarily independent or…
We address the problem of bounding below the probability of error under maximum likelihood decoding of a binary code with a known distance distribution used on a binary symmetric channel. An improved upper bound is given for the maximum…
In the current work we introduce a novel estimation of distribution algorithm to tackle a hard combinatorial optimization problem, namely the single-machine scheduling problem, with uncertain delivery times. The majority of the existing…
In this paper, we develop efficient randomized algorithms for estimating probabilistic robustness margin and constructing robustness degradation curve for uncertain dynamic systems. One remarkable feature of these algorithms is their…
In the literature there exists analytical expressions for the probability of a receiver decoding a transmitted source message that has been encoded using random linear network coding. In this work, we look into the probability that the…
A statistical estimation algorithm of the weight distribution of a linear code is shown, based on using its generator matrix as a compression function on random bit strings.
Previously referred to as `miraculous' in the scientific literature because of its powerful properties and its wide application as optimal solution to the problem of induction/inference, (approximations to) Algorithmic Probability (AP) and…
Consider a distributed coding for computing problem with constant decoding locality, i.e., with a vanishing error probability, any single sample of the function can be approximately recovered by probing only constant number of compressed…
Digital computers store information in the form of bits that can take on one of two values 0 and 1, while quantum computers are based on qubits that are described by a complex wavefunction, whose squared magnitude gives the probability of…
Suppose that we are given an infinite binary sequence which is random for a Bernoulli measure of parameter $p$. By the law of large numbers, the frequency of zeros in the sequence tends to~$p$, and thus we can get better and better…
A scheme is proposed that combines probabilistic signal shaping with bit-metric decoding. The transmitter generates symbols according to a distribution on the channel input alphabet. The symbols are labeled by bit strings. At the receiver,…
Consider binary linear codes obtained from bipartite graphs as follows. There are~\(k \geq 1\) left nodes each representing a message bit and there are~\(m = m(k)\) right nodes each representing a parity bit, generated from the…
We consider the problem of distilling uniform random bits from an unknown source with a given $p$-entropy using linear hashing. As our main result, we estimate the expected $p$-divergence from the uniform distribution over the ensemble of…
In the random deletion channel, each bit is deleted independently with probability $p$. For the random deletion channel, the existence of codes of rate $(1-p)/9$, and thus bounded away from $0$ for any $p < 1$, has been known. We give an…
Finite-precision floating point arithmetic unavoidably introduces rounding errors which are traditionally bounded using a worst-case analysis. However, worst-case analysis might be overly conservative because worst-case errors can be…
The performance of an error correcting code is evaluated by its error probability, rate, and en/decoding complexity. The performance of a series of codes is evaluated by, as the block lengths approach infinity, whether their error…
Probabilistic programming languages (PPLs) are expressive means for creating and reasoning about probabilistic models. Unfortunately hybrid probabilistic programs, involving both continuous and discrete structures, are not well supported by…
Many proofs in discrete mathematics and theoretical computer science are based on the probabilistic method. To prove the existence of a good object, we pick a random object and show that it is bad with low probability. This method is…
Text compression schemes and compact data structures usually combine sophisticated probability models with basic coding methods whose average codeword length closely match the entropy of known distributions. In the frequent case where basic…