Related papers: A Refinement of Expurgation
We derive a sphere-packing error exponent for coded transmission over discrete memoryless channels with a fixed decoding metric. By studying the error probability of the code over an auxiliary channel, we find a lower bound to the…
A conceptually simple method for derivation of lower bounds on the error exponent of specific families of block codes used on classical-quantum channels with arbitrary signal states over a finite Hilbert space is presented. It is shown that…
Consider the problem of distributed binary hypothesis testing with two terminals, where the decision is made at one of them (the "receiver"). We study the exponent of the error probability of the second type. Previously, an achievable…
We introduce a definition of perfect and quasi-perfect codes for symmetric channels parametrized by an auxiliary output distribution. This notion generalizes previous definitions of perfect and quasi-perfect codes and encompasses maximum…
We prove a strong Symmetry of Information relation for random strings (in the sense of Kolmogorov complexity) and establish tight bounds on the amount on nonuniformity that is necessary for extracting a string with randomness rate 1 from a…
This thesis presents a broad-coverage probabilistic top-down parser, and its application to the problem of language modeling for speech recognition. The parser builds fully connected derivations incrementally, in a single pass from…
We derive two conditional expectation bounds, which we use to simplify cryptographic security proofs. The first bound relates the expectation of a bounded random variable and the average of its conditional expectations with respect to a set…
This paper considers the achievability and converse bounds on the maximal channel coding rate at a given blocklength and error probability over AWGN channels. The problem stems from covert communication with Gaussian codewords. By…
Variable-length compression without prefix-free constraints and with side-information available at both encoder and decoder is considered. Instead of requiring the code to be error-free, we allow for it to have a non-vanishing error…
We introduce the factor complex of a neural code, and show how intervals and maximal codewords are captured by the combinatorics of factor complexes. We use these results to obtain algebraic and combinatorial characterizations of…
We construct a new family of explicit codes that are list decodable to capacity and achieve an optimal list size of $O(\frac{1}{\epsilon})$. In contrast to existing explicit constructions of codes achieving list decoding capacity, our…
We consider procedures of sampling parts from a random integer partition. We determine asymptotically the probabilty distribution of the randomly-selected part whenever the positive integer that is partitioned becomes large.
This paper considers the problem of variable-length lossy source coding. The performance criteria are the excess distortion probability and the cumulant generating function of codeword lengths. We derive a non-asymptotic fundamental limit…
Using tools developed in a recent work by Shen and the second author, in this paper we carry out an in-depth study on the average decoding error probability of the random matrix ensemble over the erasure channel under three decoding…
To derive a program for a given specification R means to find an artifact P that satisfies two conditions: P is executable in some programming language; and P is correct with respect to R. Refinement-based program derivation achieves this…
For the discrete memoryless sources with a countably infinite alphabet, we prove that for any positive integer $k$, there exists a corresponding probability interval such that if the largest symbol probability $p_{1}$ falls in this…
We give new bounds on the reliability function of a typewriter channel with 5 inputs and crossover probability $1/2$. The lower bound is more of theoretical than practical importance; it improves very marginally the expurgated bound,…
In this work, we derive the random coding error exponent for the uplink phase of a two-way relay system where physical layer network coding (PNC) is employed. The error exponent is derived for the practical (yet sub-optimum) XOR channel…
We study the probability that a random polynomial with integer coefficients is reducible when factored over the rational numbers. Using computer-generated data, we investigate a number of different models, including both monic and non-monic…
Hilberg's conjecture about natural language states that the mutual information between two adjacent long blocks of text grows like a power of the block length. The exponent in this statement can be upper bounded using the pointwise mutual…