Related papers: Coding for Errors and Erasures in Random Network C…
Recursive decoding techniques are considered for Reed-Muller (RM) codes of growing length $n$ and fixed order $r.$ An algorithm is designed that has complexity of order $n\log n$ and corrects most error patterns of weight up to…
We consider the problem of joint source and channel coding of structured data such as natural language over a noisy channel. The typical approach to this problem in both theory and practice involves performing source coding to first…
We study segmented burst-deletion channels motivated by the observation that synchronization errors commonly occur in a bursty manner in real-world settings. In this channel model, transmitted sequences are implicitly divided into…
We consider a set of $n$ messages and a group of $k$ clients. Each client is privileged for receiving an arbitrary subset of the messages over a broadcast erasure channel, which generalizes scenario of a previous work. We propose a method…
Linear error-correcting codes form the mathematical backbone of modern digital communication and storage systems, but identifying champion linear codes (linear codes achieving or exceeding the best known minimum Hamming distance) remains…
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 the problem of energy-efficient broadcasting on dense ad-hoc networks. Ad-hoc networks are generally modeled using random geometric graphs (RGGs). Here, nodes are deployed uniformly in a square area around the origin, and any…
We give a quantum reduction from finding short codewords in a random linear code to decoding for the Hamming metric. This is the first time such a reduction (classical or quantum) has been obtained. Our reduction adapts to linear codes…
Error-correcting codes are combinatorial objects designed to cope with the problem of reliable transmission of information on a noisy channel. A fundamental problem in coding theory and practice is to efficiently decode the received word…
We propose a hybrid protocol combining a rectangular error-correcting code - paired with an error-detecting code - and a backward error correction in order to send packages of information over a noisy channel. We depict a linear-time…
In the Levenshtein's sequence reconstruction problem a codeword is transmitted through $N$ channels and in each channel a set of errors is introduced to the transmitted word. In previous works, the restriction that each channel provides a…
In practice, since many communication networks are huge in scale, or complicated in structure, or even dynamic, the predesigned linear network codes based on the network topology is impossible even if the topological structure is known.…
Differential linear network coding (DLNC) is a precoding scheme for information transmission over random linear networks. By using differential encoding and decoding, the conventional approach of lifting, required for inherent channel…
We consider the problem of multicasting information from a source to a set of receivers over a network where intermediate network nodes perform randomized network coding operations on the source packets. We propose a channel model for the…
The advent of network coding presents promising opportunities in many areas of communication and networking. It has been recently shown that network coding technique can significantly increase the overall throughput of wireless networks by…
We provide a general framework for bounding the block error threshold of a linear code $C\subseteq \mathbb{F}_2^N$ over the erasure channel in terms of its bit error threshold. Our approach relies on understanding the minimum support weight…
A new class of folded subspace codes for noncoherent network coding is presented. The codes can correct insertions and deletions beyond the unique decoding radius for any code rate $R\in[0,1]$. An efficient interpolation-based decoding…
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…
Low-depth random circuit codes possess many desirable properties for quantum error correction but have so far only been analyzed in the code capacity setting where it is assumed that encoding gates and syndrome measurements are noiseless.…
In this work, we derive the random coding error exponent for the uplink phase of a two-way relay system where physical layer network coding (PNC) is employed. The error exponent is derived for the practical (yet sub-optimum) XOR channel…