Related papers: Function-Correcting Codes for Symbol-Pair Read Cha…
We examine an error-correcting coding framework in which each coded symbol is constrained to be a function of a fixed subset of the message symbols. With an eye toward distributed storage applications, we seek to design systematic codes…
Function-correcting codes with data protection simultaneously protect both the data and a function of the data at distinct error-correction levels. When the function receives strictly stronger protection than the data, such a code is called…
We introduce two notions of discrepancy between binary vectors, which are not metric functions in general but nonetheless capture the mathematical structure of the binary asymmetric channel. In turn, these lead to two new fundamental…
Symbol-pair codes are proposed to guard against pair-errors in symbol-pair read channels. The minimum symbol-pair distance is of significance in determining the error-correcting capability of a symbol-pair code. One of the central themes in…
Symbol-pair codes are proposed to protect against pair errors in symbol-pair read channels. One of the most important task in symbol-pair coding theory is to determine the minimum pair-distance of symbol-pair codes. In this paper, we…
Symbol-pair codes are proposed to guard against pair-errors in symbol-pair read channels. The minimum symbol-pair distance plays a vital role in determining the error-correcting capability and the constructions of symbol-pair codes with…
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…
This paper computationally obtains optimal bounded-weight, binary, error-correcting codes for a variety of distance bounds and dimensions. We compare the sizes of our codes to the sizes of optimal constant-weight, binary, error-correcting…
In this paper, we introduce a class of functions that assume only a limited number $\lambda$ of values within a given Hamming $\rho$-ball and call them locally $(\rho, \lambda)$-bounded functions. We develop function-correcting codes (FCCs)…
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…
The family of functions plays a central role in the design and effectiveness of function-correcting codes. By focusing on a well-defined family of functions, function-correcting codes can be constructed with minimal length while still…
Symbol-pair codes are block codes with symbol-pair metrics designed to protect against pair-errors that may occur in high-density data storage systems. MDS symbol-pair codes are optimal in the sense that it can attain the highest pair-error…
Rate-compatible error-correcting codes (ECCs), which consist of a set of extended codes, are of practical interest in both wireless communications and data storage. In this work, we first study the lower bounds for rate-compatible ECCs,…
Linear codes generated by component functions of perfect nonlinear (PN) and almost perfect nonlinear (APN) functions and the first-order Reed-Muller codes have been an object of intensive study in coding theory. The objective of this paper…
In classical coding theory, error-correcting codes are designed to protect against errors occurring at individual symbol positions in a codeword. However, in practical storage and communication systems, errors often affect multiple adjacent…
We consider data transmission over a network where each edge is an erasure channel and where the inner nodes transmit a random linear combination of their incoming information. We distinguish two channel models in this setting, the row and…
The construction of asymmetric error correcting codes is a topic that was studied extensively, however, the existing approach for code construction assumes that every codeword should tolerate $t$ asymmetric errors. Our main observation is…
The weighted-Hamming metric generalizes the Hamming metric by assigning different weights to blocks of coordinates. It is well-suited for applications such as coding over independent parallel channels, each of which has a different level of…
The high-density data storage technology aims to design high-capacity storage at a relatively low cost. In order to achieve this goal, symbol-pair codes were proposed by Cassuto and Blaum \cite{CB10,CB11} to handle channels that output…
Independent parallel q-ary symmetric channels are a suitable transmission model for several applications. The proposed weighted-Hamming metric is tailored to this setting and enables optimal decoding performance. We show that some…