Related papers: On Unique Decodability
We study uniquely decodable codes and list decodable codes in the high-noise regime, specifically codes that are uniquely decodable from $\frac{1-\varepsilon}{2}$ fraction of errors and list decodable from $1-\varepsilon$ fraction of…
Reed--Solomon error-correcting codes are ubiquitous across computer science and information theory, with applications in cryptography, computational complexity, communication and storage systems, and more. Most works on efficient error…
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…
In this paper we consider lossless source coding for a class of sources specified by the total variational distance ball centred at a fixed nominal probability distribution. The objective is to find a minimax average length source code,…
We consider a problem in which a source is encoded into N packets, an unknown number of which are subject to adversarial errors en route to the decoder. We seek code designs for which the decoder is guaranteed to be able to reproduce the…
Bounds on the reliability function for the discrete memoryless relay channel are derived using the method of types. Two achievable error exponents are derived based on partial decode-forward and compress-forward which are well-known…
We initiate a study of locally decodable codes with randomized encoding. Standard locally decodable codes are error correcting codes with a deterministic encoding function and a randomized decoding function, such that any desired message…
Error correction codes are a crucial part of the physical communication layer, ensuring the reliable transfer of data over noisy channels. The design of optimal linear block codes capable of being efficiently decoded is of major concern,…
In this paper, we study how often unique decoding from $t$ insertions or $t$ deletions occurs for error correcting codes. Insertions and deletions frequently occur in synchronization problems and DNA, a medium which is beginning to be used…
We study the channel coding problem when errors and uncertainty occur in the encoding process. For simplicity we assume the channel between the encoder and the decoder is perfect. Focusing on linear block codes, we model the encoding…
This paper deals with a universal coding problem for a certain kind of multiterminal source coding system that we call the complementary delivery coding system. In this system, messages from two correlated sources are jointly encoded, and…
We consider the problem of erasure/list decoding using certain classes of simplified decoders. Specifically, we assume a class of erasure/list decoders, such that a codeword is in the list if its likelihood is larger than a threshold. This…
The optimal causal coding of a partially observed Markov process is studied, where the cost to be minimized is a bounded, non-negative, additive, measurable single-letter function of the source and the receiver output. A structural result…
We consider a decoder with an erasure option and a variable size list decoder for channels with non-casual side information at the transmitter. First, universally achievable error exponents are offered for decoding with an erasure option…
Motivated by distributed storage applications, we investigate the degree to which capacity achieving encodings can be efficiently updated when a single information bit changes, and the degree to which such encodings can be efficiently…
We study universal compression of sequences generated by monotonic distributions. We show that for a monotonic distribution over an alphabet of size $k$, each probability parameter costs essentially $0.5 \log (n/k^3)$ bits, where $n$ is the…
We investigate adaptive single-trial error/erasure decoding of binary codes whose decoder is able to correct e errors and t erasures if le+t<=d-1. Thereby, d is the minimum Hamming distance of the code and 1<l<=2 is the tradeoff parameter…
We consider the problem of constructing codes that can correct deletions that are localized within a certain part of the codeword that is unknown a priori. Namely, the model that we study is when at most $k$ deletions occur in a window of…
The Shannon Noiseless coding theorem (the data-compression principle) asserts that for an information source with an alphabet $\mathcal X=\{0,\ldots ,\ell -1\}$ and an asymptotic equipartition property, one can reduce the number of stored…
This paper investigates variable-length stop-feedback codes for memoryless channels in point-to-point, multiple access, and random access communication scenarios. The proposed codes employ $L$ decoding times $n_1, n_2, \dots, n_L$ for the…