Related papers: Channels with Synchronization/Substitution Errors …
Consider the following unequal error protection scenario. One special message, dubbed the "red alert" message, is required to have an extremely small probability of missed detection. The remainder of the messages must keep their average…
A binary code of blocklength $n$ and codebook size $M$ is called an $(n,M)$ code, which is studied for memoryless binary symmetric channels (BSCs) with the maximum likelihood (ML) decoding. For any $n \geq 2$, some optimal codes among the…
In the paper, the Levenshtein's sequence reconstruction problem is considered in the case where at most $t$ substitution errors occur in each of the $N$ channels and the decoder outputs a list of length $\mathcal{L}$. Moreover, it is…
We examine the efficiency of pure, nondegenerate quantum-error correction-codes for Pauli channels. Specifically, we investigate if correction of multiple errors in a block is more efficient than using a code that only corrects one error…
A central question in information theory is to determine the maximum success probability that can be achieved in sending a fixed number of messages over a noisy channel. This was first studied in the pioneering work of Shannon who…
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…
Randomized techniques play a fundamental role in theoretical computer science and discrete mathematics, in particular for the design of efficient algorithms and construction of combinatorial objects. The basic goal in derandomization theory…
Channel capacities quantify the optimal rates of sending information reliably over noisy channels. Usually, the study of capacities assumes that the circuits which sender and receiver use for encoding and decoding consist of perfectly…
A new universal coding/decoding scheme for random access with collision detection is given in the case of two senders. The result is used to give an achievable joint source-channel coding error exponent for multiple access channels in the…
We consider a new formulation of a class of synchronization error channels and derive analytical bounds and numerical estimates for the capacity of these channels. For the binary channel with only deletions, we obtain an expression for the…
The problem of error control in random linear network coding is addressed from a matrix perspective that is closely related to the subspace perspective of K\"otter and Kschischang. A large class of constant-dimension subspace codes is…
In this paper, we consider a concatenated coding based class of DNA storage codes in which the selected molecules are constrained to be taken from an ``inner'' codebook associated with the sequencing channel. This codebook is used in a…
This paper considers error probabilities of random codes for memoryless channels in the fixed-rate regime. Random coding is a fundamental scheme to achieve the channel capacity and many studies have been conducted for the asymptotics of the…
In this work, we introduce convolutional codes for network-error correction in the context of coherent network coding. We give a construction of convolutional codes that correct a given set of error patterns, as long as consecutive errors…
We study the error detection problem in $ q $-ary asymmetric channels wherein every input symbol $ x_i $ is mapped to an output symbol $ y_i $ satisfying $ y_i \geq x_i $. A general setting is assumed where the noise vectors are…
We develop a theory for finding quantum error correction (QEC) procedures which are optimized for given noise channels. Our theory accounts for uncertainties in the noise channel, against which our QEC procedures are robust. We demonstrate…
A rateless code encodes a finite length information word into an infinitely long codeword such that longer prefixes of the codeword can tolerate a larger fraction of errors. A rateless code achieves capacity for a family of channels if, for…
Use of an error correction code in a given transmission channel can be regarded as the statistical experiment. Therefore, powerful results from the theory of comparison of experiments can be applied to compare the performances of different…
We study iterative blind symbol detection for block-fading linear inter-symbol interference channels. Based on the factor graph framework, we design a joint channel estimation and detection scheme that combines the expectation maximization…
In a recent paper ([1]=quant-ph/0606035) it is shown how the optimal recovery operation in an error correction scheme can be considered as a semidefinite program. As a possible future improvement it is noted that still better error…