Related papers: Channel Coding based on Skew Polynomials and Multi…
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 give a polynomial time algorithm to decode multivariate polynomial codes of degree $d$ up to half their minimum distance, when the evaluation points are an arbitrary product set $S^m$, for every $d < |S|$. Previously known algorithms can…
A modification of Koetter-Kschischang codes for random networks is presented (these codes were also studied by Wang et al. in the context of authentication problems). The new codes have higher information rate, while maintaining the same…
Regenerating codes provide an efficient way to recover data at failed nodes in distributed storage systems. It has been shown that regenerating codes can be designed to minimize the per-node storage (called MSR) or minimize the…
Motivated by applications of distributed storage systems to key-value stores, the multi-version coding problem was formulated to efficiently store frequently updated data in asynchronous decentralized storage systems. Inspired by…
In this paper we introduce the class of Spread Codes for the use in random network coding. Spread Codes are based on the construction of spreads in finite projective geometry. The major contribution of the paper is an efficient decoding…
In this paper, channel optimized distributed multiple description vector quantization (CDMD) schemes are presented for distributed source coding in symmetric and asymmetric settings. The CDMD encoder is designed using a deterministic…
We consider the decoding of linear and array codes from errors when we are only allowed to download a part of the codeword. More specifically, suppose that we have encoded $k$ data symbols using an $(n,k)$ code with code length $n$ and…
Skew polynomial rings provide a fundamental example of noncommutative principal ideal domains. Special quotients of these rings yield matrix algebras that play a central role in the theory of rank-metric codes. Recent breakthroughs have…
Sum-rank-metric codes have wide applications in the multishot network coding and the distributed storage. Linearized Reed-Solomon codes, sum-rank BCH codes and their Welch-Berlekamp type decoding algorithms were proposed and studied. They…
Error-correcting codes and related combinatorial constructs play an important role in several recent (and old) results in computational complexity theory. In this paper we survey results on locally-testable and locally-decodable…
We propose new repair schemes for Reed-Solomon codes that use subspace polynomials and hence generalize previous works in the literature that employ trace polynomials. The Reed-Solomon codes are over $\mathbb{F}_{q^\ell}$ and have…
Distributed source coding schemes are typically based on the use of channels codes as source codes. In this paper we propose a new paradigm, termed "distributed arithmetic coding", which exploits the fact that arithmetic codes are good…
Generalized Reed-Solomon (RS) codes are a common choice for efficient, reliable error correction in memory and communications systems. These codes add $2t$ extra parity symbols to a block of memory, and can efficiently and reliably correct…
This paper addresses network code design for robust transmission of sources over an orthogonal two-hop wireless network with a broadcasting relay. The network consists of multiple sources and destinations in which each destination,…
Error correcting codes play a central role in digital communication, ensuring that transmitted information can be accurately reconstructed despite channel impairments. Recently, autoencoder (AE) based approaches have gained attention for…
Ternary channels can be used to model the behavior of some memory devices, where information is stored in three different levels. In this paper, error correcting coding for a ternary channel where some of the error transitions are not…
This paper presents a novel coding scheme for distributed storage systems containing nodes with adversarial errors. The key challenge in such systems is the propagation of erroneous data from a single corrupted node to the rest of the…
We study the numerical stability of polynomial based encoding methods, which has emerged to be a powerful class of techniques for providing straggler and fault tolerance in the area of coded computing. Our contributions are as follows: 1)…
While feasibility and obtaining a solution of a given network coding problem are well studied, the decoding procedure and complexity have not garnered much attention. We consider the decoding problem in a network wherein the sources…