Related papers: Concentration Properties of Random Codes
Floating-point round-off errors are ubiquitous in numerically intensive programs arising in fields such as scientific computing and optimization. As floating-point errors potentially lead to unexpected and catastrophic program failures, one…
The identification capacity region of the compound broadcast channel is determined under an average error criterion, where the sender has no channel state information. We give single-letter identification capacity formulas for discrete…
Shaping codes are used to encode information for use on channels with cost constraints. Applications include data transmission with a power constraint and, more recently, data storage on flash memories with a constraint on memory cell wear.…
This paper provides a dual domain derivation of the error exponent of maximum mutual information (MMI) decoding with constant composition codes, showing it coincides with that of maximum likelihood decoding for discrete memoryless channels.…
Traditional studies of multi-source, multi-terminal interference channels typically allow a vanishing probability of error in communication. Motivated by the study of network coding, this work addresses the task of quantifying the loss in…
We consider communication over binary-input memoryless output-symmetric channels using low-density parity-check codes and message-passing decoding. The asymptotic (in the length) performance of such a combination for a fixed number of…
We examine regular and irregular repeat-accumulate (RA) codes with repetition degrees which are all even. For these codes and with a particular choice of an interleaver, we give an upper bound on the decoding error probability of a…
We initiate the probabilistic analysis of linear programming (LP) decoding of low-density parity-check (LDPC) codes. Specifically, we show that for a random LDPC code ensemble, the linear programming decoder of Feldman et al. succeeds in…
We consider the one helper source coding problem posed and investigated by Ahlswede, K\"orner and Wyner. In this system, the error probability of decoding goes to one as the source block length $n$ goes to infinity. This implies that we…
It was recently shown that spatial coupling of individual low-density parity-check codes improves the belief-propagation threshold of the coupled ensemble essentially to the maximum a posteriori threshold of the underlying ensemble. We…
We consider the secret key generation problem when sources are randomly excited by the sender and there is a noiseless public discussion channel. Our setting is thus similar to recent works on channels with action-dependent states where the…
Random Number Generators play a critical role in a number of important applications. In practice, statistical testing is employed to gather evidence that a generator indeed produces numbers that appear to be random. In this paper, we…
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…
Through refined asymptotic analysis based on the normal approximation, we study how higher-order coding performance depends on the mean power as well as on finer statistics of the input power. We introduce a multifaceted power model in…
This paper presents prefix codes which minimize various criteria constructed as a convex combination of maximum codeword length and average codeword length or maximum redundancy and average redundancy, including a convex combination of the…
Convexity properties of error rates of a class of decoders, including the ML/min-distance one as a special case, are studied for arbitrary constellations, bit mapping and coding. Earlier results obtained for the AWGN channel are extended to…
We examine the concentration of uniform generalization errors around their expectation in binary linear classification problems via an isoperimetric argument. In particular, we establish Poincar\'{e} and log-Sobolev inequalities for the…
Error correction codes are an integral part of communication applications, boosting the reliability of transmission. The optimal decoding of transmitted codewords is the maximum likelihood rule, which is NP-hard due to the curse of…
We consider irregular product codes.In this class of codes, each codeword is represented by a matrix. The entries in each row (column) of the matrix should come from a component row (column) code. As opposed to (standard) product codes, we…
In this work we investigate the behavior of the distortion threshold that can be guaranteed in joint source-channel coding, to within a prescribed excess-distortion probability. We show that the gap between this threshold and the optimal…