Related papers: Index Coding and Error Correction
Labeling of DNA molecules is a fundamental technique for DNA visualization and analysis. This process was mathematically modeled in [1], where the received sequence indicates the positions of the used labels. In this work, we develop error…
It is well known that no quantum error correcting code of rate $R$ can correct adversarial errors on more than a $(1-R)/4$ fraction of symbols. But what if we only require our codes to *approximately* recover the message? We construct…
In this paper, we investigate the problem of recovering source information from an incomplete set of network coded data. We first study the theoretical performance of such systems under maximum a posteriori (MAP) decoding and derive the…
Maximum run-length limited codes are constraint codes used in communication and data storage systems. Insertion/deletion correcting codes correct insertion or deletion errors caused in transmitted sequences and are used for combating…
This paper studies index coding with two senders. In this setup, source messages are distributed among the senders possibly with common messages. In addition, there are multiple receivers, with each receiver having some messages a priori,…
We study coding schemes for error correction in interactive communications. Such interactive coding schemes simulate any $n$-round interactive protocol using $N$ rounds over an adversarial channel that corrupts up to $\rho N$ transmissions.…
Subspace codes and rank-metric codes can be used to correct errors and erasures in network, with linear network coding. Subspace codes were introduced by Koetter and Kschischang to correct errors and erasures in networks where topology is…
We characterise bounds on the optimal broadcast rate for a few classes of pliable-index-coding instances. Unlike the majority of currently solved instances, which belong to a special class where all receivers with a certain side-information…
In this work we investigate codes in $\mathbb{Z}_{2^m}^n$ that can correct errors that occur in just one coordinate of the codeword, with a magnitude of up to a given parameter $t$. We will show upper bounds on these cross codes, derive…
We study the index coding problem in the presence of an eavesdropper, where the aim is to communicate without allowing the eavesdropper to learn any single message aside from the messages it may already know as side information. We…
We study the zero-error source coding problem in which an encoder with Side Information (SI) $g(Y)$ transmits source symbols $X$ to a decoder. The decoder has SI $Y$ and wants to recover $f(X,Y)$ where $f,g$ are deterministic. We exhibit a…
Motivated by applications to distributed storage, Gopalan \textit{et al} recently introduced the interesting notion of information-symbol locality in a linear code. By this it is meant that each message symbol appears in a parity-check…
This paper studies noisy index coding problems over single-input single-output broadcast channels. The codewords from a chosen index code of length $N$ are transmitted after $2^N$-PSK modulation over an AWGN channel. In "Index Coded PSK…
Index Coding has received considerable attention recently motivated in part by real-world applications and in part by its connection to Network Coding. The basic setting of Index Coding encodes the problem input as an undirected graph and…
In this paper, we prove that with high probability, random Reed-Solomon codes approach the half-Singleton bound - the optimal rate versus error tradeoff for linear insdel codes - with linear-sized alphabets. More precisely, we prove that,…
We construct constant-sized ensembles of linear error-correcting codes over any fixed alphabet that can correct a given fraction of adversarial erasures at rates approaching the Singleton bound arbitrarily closely. We provide several…
Interleaved Reed-Solomon codes admit efficient decoding algorithms which correct burst errors far beyond half the minimum distance in the random errors regime, e.g., by computing a common solution to the Key Equation for each Reed-Solomon…
The index coding problem is concerned with broadcasting encoded information to a collection of receivers in a way that enables each receiver to discover its required data based on its side information, which comprises the data required by…
In this paper, we study the upper and the lower bounds on the joint source-channel coding error exponent with decoder side-information. The results in the paper are non-trivial extensions of the Csiszar's classical paper [5]. Unlike the…
For index coding problems with special structure on the side-information graphs called Interlinked Cycle (IC) structures index codes have been proposed in the literature (C. Thapa, L. Ong, and S. Johnson, "Interlinked Cycles for Index…