Related papers: Efficient Evaluation of the Probability of Error o…
New upper and lower bounds for the error probability over an erasure channel are provided, making use of Wei's generalized weights, hierarchy and spectra. In many situations the upper and lower bounds coincide and this allows improvement of…
We prove the following results concerning the list decoding of error-correcting codes: (i) We show that for \textit{any} code with a relative distance of $\delta$ (over a large enough alphabet), the following result holds for \textit{random…
The error coefficient of a linear code is defined as the number of minimum-weight codewords. In an additive white Gaussian noise channel, optimal linear codes with the smallest error coefficients achieve the best possible asymptotic frame…
This paper studies the parameters for which Reed-Muller (RM) codes over $GF(2)$ can correct random erasures and random errors with high probability, and in particular when can they achieve capacity for these two classical channels.…
We present a general approach to deriving bounds on the generalization error of randomized learning algorithms. Our approach can be used to obtain bounds on the average generalization error as well as bounds on its tail probabilities, both…
When information is to be transmitted over an unknown, possibly unreliable channel, an erasure option at the decoder is desirable. Using constant-composition random codes, we propose a generalization of Csiszar and Korner's Maximum Mutual…
We study error bounds for linear programming decoding of regular LDPC codes. For memoryless binary-input output-symmetric channels, we prove bounds on the word error probability that are inverse doubly-exponential in the girth of the factor…
In this paper, we compute the tightest possible bounds on the probability that the optimal value of a combinatorial optimization problem in maximization form with a random objective exceeds a given number, assuming only knowledge of the…
It is common practice to collect observations of feature and response pairs from different environments. A natural question is how to identify features that have consistent prediction power across environments. The invariant causal…
Determining the exact decoding error probability of linear block codes is an interesting problem. For binary BCH codes, McEliece derived methods to estimate the error probability of a simple bounded distance decoding (BDD) for BCH codes.…
In this paper, we present a novel way for solving the main problem of designing the capacity approaching irregular low-density parity-check (LDPC) code ensemble over binary erasure channel (BEC). The proposed method is much simpler, faster,…
The problem of blind identification of channel codes at a receiver involves identifying a code chosen by a transmitter from a known code-family, by observing the transmitted codewords through the channel. Most existing approaches for…
Coherent lower previsions are general probabilistic models allowing incompletely specified probability distributions. However, for complete description of a coherent lower prevision -- even on finite underlying sample spaces -- an infinite…
The Poltyrev bound provides a very tight upper bound on the decoding error probability when using binary linear codes for transmission over the binary symmetric channel and the additive white Gaussian noise channel, making use of the code's…
We propose two types of universal codes that are suited to two asymptotic regimes when the output alphabet is possibly continuous. The first class has the property that the error probability decays exponentially fast and we identify an…
This paper applies error-exponent and dispersion-style analyses to derive finite-blocklength achievability bounds for low-density parity-check (LDPC) codes over the point-to-point channel (PPC) and multiple access channel (MAC). The…
In this work, we consider efficient maximum-likelihood decoding of linear block codes for small-to-moderate block lengths. The presented approach is a branch-and-bound algorithm using the cutting-plane approach of Zhang and Siegel (IEEE…
There is a known best possible upper bound on the probability of undetected error for linear codes. The $[n,k;q]$ codes with probability of undetected error meeting the bound have support of size $k$ only. In this note, linear codes of full…
Sparse superposition codes, or sparse regression codes (SPARCs), are a recent class of codes for reliable communication over the AWGN channel at rates approaching the channel capacity. Approximate message passing (AMP) decoding, a…
We consider a communication problem in which the receiver must first detect the presence of an information packet and, if detected, decode the message carried within it. We present general nonasymptotic upper and lower bounds on the maximum…