Related papers: Plotkin-like Bound and Explicit Function-Correctin…
A $q$-ary $(n,k,r)$ locally repairable code (LRC) is an $[n,k,d]$ linear code over $\mathbb{F}_q$ such that every code symbol can be recovered by accessing at most $r$ other code symbols. The well-known Singleton-like bound says that $d \le…
This work is motivated by the problem of error correction in bit-shift channels with the so-called $ (d,k) $ input constraints (where successive $ 1 $'s are required to be separated by at least $ d $ and at most $ k $ zeros, $ 0 \leq d < k…
Block codes, which correct asymmetric errors with limited-magnitude, are studied. These codes have been applied recently for error correction in flash memories. The codes will be represented by lattices and the constructions will be based…
Codes in the projective space and codes in the Grassmannian over a finite field - referred to as subspace codes and constant-dimension codes (CDCs), respectively - have been proposed for error control in random linear network coding. For…
Designing channel codes under low-latency constraints is one of the most demanding requirements in 5G standards. However, a sharp characterization of the performance of traditional codes is available only in the large block-length limit.…
This study investigates the capabilities of Cyclic Redundancy Checks(CRCs) to detect burst and random errors. Researchers have favored these error detection codes throughout the evolution of computing and have implemented them in…
As a medium for cold data storage, DNA stands out as it promises significant gains in storage capacity and lifetime. However, it comes with its own data processing challenges to overcome. Constrained codes over the DNA alphabet…
The design of block codes for short information blocks (e.g., a thousand or less information bits) is an open research problem that is gaining relevance thanks to emerging applications in wireless communication networks. In this paper, we…
Short circuit fault currents are increasing due to growing demand for electricity and high complexity in power systems. Because the fault currents reach the highest value which the breakers are unable to restrict, the electrical grid…
Locally Decodable Codes (LDCs) are error-correcting codes $C\colon\Sigma^n\rightarrow \Sigma^m,$ encoding \emph{messages} in $\Sigma^n$ to \emph{codewords} in $\Sigma^m$, with super-fast decoding algorithms. They are important mathematical…
The growing demand for highly reliable communication systems drives the research and development of algorithms that identify and correct errors during data transmission and storage. This need becomes even more critical in hard-to-access or…
Locally repairable codes (LRCs) with $(r,\delta)$ locality were introduced by Prakash \emph{et al.} into distributed storage systems (DSSs) due to their benefit of locally repairing at least $\delta-1$ erasures via other $r$ survival nodes…
LDPC (Low Density Parity Check) codes are among the most powerful and widely adopted modern error correcting codes. The iterative decoding algorithms required for these codes involve high computational complexity and high processing…
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…
LDPC codes play a vital role in coding theory and practical error correction. A central problem in this direction is to understand their rate--distance tradeoff. In this paper, we introduce a new framework for estimating ball sizes in the…
Chunked codes are efficient random linear network coding (RLNC) schemes with low computational cost, where the input packets are encoded into small chunks (i.e., subsets of the coded packets). During the network transmission, RLNC is…
We study the Singleton-type bound that provides an upper limit on the minimum distance of locally repairable codes. We present an improved bound by carefully analyzing the combinatorial structure of the repair sets. Thus, we show the…
We demonstrate that error correcting codes (ECCs) can be used to construct a labeled data set for finetuning of "trainable" communication systems without sacrificing resources for the transmission of known symbols. This enables adaptive…
Locally decodable codes (LDCs) are error correcting codes that allow for decoding of a single message bit using a small number of queries to a corrupted encoding. Despite decades of study, the optimal trade-off between query complexity and…
This paper presents a theoretical study of a new type of LDPC codes motivated by practical storage applications. LDPCL codes (suffix L represents locality) are LDPC codes that can be decoded either as usual over the full code block, or…