Related papers: Another look at expurgated bounds and their statis…
This paper determines the range of feasible values of standard error exponents for binary-input memoryless symmetric channels of fixed capacity $C$ and shows that extremes are attained by the binary symmetric and the binary erasure channel.…
The distributed hypothesis testing problem with full side-information is studied. The trade-off (reliability function) between the two types of error exponents under limited rate is studied in the following way. First, the problem is…
We derive generic information-theoretic and PAC-Bayesian generalization bounds involving an arbitrary convex comparator function, which measures the discrepancy between the training and population loss. The bounds hold under the assumption…
The trapping redundancy of a linear code is the number of rows of a smallest parity-check matrix such that no submatrix forms an $(a,b)$-trapping set. This concept was first introduced in the context of low-density parity-check (LDPC) codes…
We present a general method for deriving collapsed variational inference algo- rithms for probabilistic models in the conjugate exponential family. Our method unifies many existing approaches to collapsed variational inference. Our…
The performance of Gallager's error-correcting code is investigated via methods of statistical physics. In this approach, the transmitted codeword comprises products of the original message bits selected by two randomly-constructed sparse…
We study the problem of numerical differentiation of functions from weighted Wiener classes. We construct and analyze a truncation Legendre method to recover arbitrary order derivatives. The main focus is on obtaining error estimates in…
Bayesian classification labels observations based on given prior information, namely class-a priori and class-conditional probabilities. Bayes' risk is the minimum expected classification cost that is achieved by the Bayes' test, the…
In this paper, we develop a general approach for probabilistic estimation and optimization. An explicit formula and a computational approach are established for controlling the reliability of probabilistic estimation based on a mixed…
A lower bound on the number of uncorrectable errors of weight half the minimum distance is derived for binary linear codes satisfying some condition. The condition is satisfied by some primitive BCH codes, extended primitive BCH codes,…
This paper presents new lower and upper bounds for the optimal compression of binary prefix codes in terms of the most probable input symbol, where compression efficiency is determined by the nonlinear codeword length objective of…
Convex sample approximations of chance-constrained optimization problems are considered, in which chance constraints are replaced by sets of sampled constraints. We propose a randomized sample selection strategy that allows tight bounds to…
We find the exact typical error exponent of constant composition generalized random Gilbert-Varshamov (RGV) codes over DMCs channels with generalized likelihood decoding. We show that the typical error exponent of the RGV ensemble is equal…
In this work, a new upper bound for average error probability of a two-user discrete memoryless (DM) multiple-access channel (MAC) is derived. This bound can be universally obtained for all discrete memoryless MACs with given input and…
A concatenated coding scheme over binary memoryless symmetric (BMS) channels using a polarization transformation followed by outer sub-codes is analyzed. Achievable error exponents and upper bounds on the error rate are derived. The first…
In this paper, we study a strong inverse approximation theorem and saturation order for the family of Kantorovich exponential sampling operators. The class of log-uniformly continuous and bounded functions, and class of log-H\"{o}lderian…
We study exponential sums of the form $\sum_{n=1}^N e^{2\pi i a b^n/m}$ for non-zero integers $a,b,m$. Classically, non-trivial bounds were known for $N\ge \sqrt{m}$ by Korobov, and this range has been extended significantly by Bourgain as…
We consider a broadcast channel with a degraded message set, in which a single transmitter sends a common message to two receivers and a private message to one of the receivers only. The main goal of this work is to find new lower bounds to…
We analyse the forward error in the floating point summation of real numbers, from algorithms that do not require recourse to higher precision or better hardware. We derive informative explicit expressions, and new deterministic and…
Error bounds, which refer to inequalities that bound the distance of vectors in a test set to a given set by a residual function, have proven to be extremely useful in analyzing the convergence rates of a host of iterative methods for…