Related papers: Decoding Error Probability of the Random Matrix En…
An erasure channel with a fixed alphabet size $q$, where $q \gg 1$, is studied. It is proved that over any erasure channel (with or without memory), Maximum Distance Separable (MDS) codes achieve the minimum probability of error (assuming…
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…
We consider communication over the binary erasure channel (BEC) using low-density parity-check (LDPC) code and belief propagation (BP) decoding. The bit error probability for infinite block length is known by density evolution and it is…
The analysis of random coding error exponents pertaining to erasure/list decoding, due to Forney, is revisited. Instead of using Jensen's inequality as well as some other inequalities in the derivation, we demonstrate that an exponentially…
The DNA storage channel is considered, in which a codeword is comprised of $M$ unordered DNA molecules. At reading time, $N$ molecules are sampled with replacement, and then each molecule is sequenced. A coded-index concatenated-coding…
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 consider ensembles of channel codes that are partitioned into bins, and focus on analysis of exact random coding error exponents associated with optimum decoding of the index of the bin to which the transmitted codeword belongs. Two main…
Exponential error bounds for the finite-alphabet interference channel (IFC) with two transmitter-receiver pairs, are investigated under the random coding regime. Our focus is on optimum decoding, as opposed to heuristic decoding rules that…
Computation of the undetected error probability for error correcting codes over the Z-channel is an important issue, explored only in part in previous literature. In this paper we consider the case of Varshamov-Tenengol'ts codes, by…
Surface codes are among the best candidates to ensure the fault-tolerance of a quantum computer. In order to avoid the accumulation of errors during a computation, it is crucial to have at our disposal a fast decoding algorithm to quickly…
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…
For the information transmission over a binary symmetric channel the random coding is used. The transmission of exponential number of messages is considered. The exact decoding error probability exponent is derived. The proof is based on…
We consider a generalization of the discrete memoryless channel, in which the channel probability distribution is replaced by a uniform distribution over clouds of channel output sequences. For a random ensemble of such channels, we derive…
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…
This paper shows that the probability that the error exponent of a given code randomly generated from a pairwise independent ensemble being smaller than a lower bound on the typical random-coding exponent tends to zero as the codeword…
I. This paper is devoted to the problem of error detection with quantum codes. In the first part we examine possible problem settings for quantum error detection. Our goal is to derive a functional that describes the probability of…
Consider the asymmetric broadcast channel with a random superposition codebook, which may be comprised of constant composition or \iid codewords. By applying Forney's optimal decoder for individual messages and the message pair for the…
Typical random codes (TRC) in a communication scenario of source coding with side information at the decoder is the main subject of this work. We study the semi-deterministic code ensemble, which is a certain variant of the ordinary random…
Consider the following framework of universal decoding suggested in [MerhavUniversal]. Given a family of decoding metrics and random coding distribution (prior), a single, universal, decoder is optimal if for any possible channel the…
Characterization of the delay profile of systems employing random linear network coding is important for the reliable provision of broadcast services. Previous studies focused on network coding over large finite fields or developed Markov…