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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…
In this work, we present a new version of non-binary VT codes that are capable of correcting a single deletion or single insertion. Moreover, we provide the first known linear time algorithms that encode user messages into these codes of…
A permutation code is a nonlinear code whose codewords are permutation of a set of symbols. We consider the use of permutation code in the deletion channel, and consider the symbol-invariant error model, meaning that the values of the…
Recent work by Smagloy et al. (ISIT 2020) shows that the redundancy of a single-deletion $s$-substitution correcting code is asymptotically at least $(s+1)\log n+o(\log n)$, where $n$ is the length of the codes. They also provide a…
Optimal dense coding using a partially-entangled pure state of Schmidt rank $\bar D$ and a noiseless quantum channel of dimension $D$ is studied both in the deterministic case where at most $L_d$ messages can be transmitted with perfect…
Achieving agreement among distributed parties is a fundamental task in modern systems, underpinning applications such as consensus in blockchains, coordination in cloud infrastructure, and fault tolerance in critical services. However, this…
Subspace codes form the appropriate mathematical setting for investigating the Koetter-Kschischang model of fault-tolerant network coding. The Main Problem of Subspace Coding asks for the determination of a subspace code of maximum size…
In this paper, we investigate the optimum way to allocate redundancy of finite-length nested codes for modern nonvolatile memories suffering from both permanent defects and transient errors (erasures or random errors). A nested coding…
The rank modulation scheme has been proposed for efficient writing and storing data in non-volatile memory storage. Error-correction in the rank modulation scheme is done by considering permutation codes. In this paper we consider codes in…
An error correcting code ($\mathsf{ECC}$) allows a sender to send a message to a receiver such that even if a constant fraction of the communicated bits are corrupted, the receiver can still learn the message correctly. Due to their…
In steganography, we always hope to maximize the embedding payload subject to an upper-bounded distortion. We need suitable distortion measurement to evaluate the embedding impact. However, different distortion functions exposes different…
Data synchronization is a fundamental problem with applications in diverse fields such as cloud storage, genomics, and distributed systems. This paper addresses the challenge of synchronizing two files, one of which is a subsequence of the…
We consider a binary erasure version of the n-channel multiple descriptions problem with symmetric descriptions, i.e., the rates of the n descriptions are the same and the distortion constraint depends only on the number of messages…
Self-stabilizing protocols enable distributed systems to recover correct behavior starting from any arbitrary configuration. In particular, when processors communicate by message passing, fake messages may be placed in communication links…
Function-correcting codes, introduced by Lenz, Bitar, Wachter-Zeh, and Yaakobi, protect specific function values of a message rather than the entire message. A central challenge is determining the optimal redundancy -- the minimum…
We consider the problem of computing a maximal matching with a distributed algorithm in the presence of batch-dynamic changes to the graph topology. We assume that a graph of $n$ nodes is vertex-partitioned among $k$ players that…
In this paper, we consider a synchronization problem between nodes $A$ and $B$ that are connected through a two--way communication channel. {Node $A$} contains a binary file $X$ of length $n$ and {node $B$} contains a binary file $Y$ that…
In this paper, we introduce a new practical and general method for solving the main problem of designing the capacity approaching, optimal rate, irregular low-density parity-check (LDPC) code ensemble over binary erasure channel (BEC).…
We present new lower and upper bounds for the compression rate of binary prefix codes optimized over memoryless sources according to two related exponential codeword length objectives. The objectives explored here are exponential-average…
Consider two remote nodes having binary sequences $X$ and $Y$, respectively. $Y$ is an edited version of ${X}$, where the editing involves random deletions, insertions, and substitutions, possibly in bursts. The goal is for the node with…