相关论文: Guess & Check Codes for Deletions, Insertions, and…
In this paper, we propose a new erasure decoding algorithm for convolutional codes using the generator matrix. This implies that our decoding method also applies to catastrophic convolutional codes in opposite to the classic approach using…
In this work, we study linear error-correcting codes against adversarial insertion-deletion (insdel) errors, a topic that has recently gained a lot of attention. We construct linear codes over $\mathbb{F}_q$, for…
The performance of Reed--Solomon codes (RS codes, for short) in the presence of insertion and deletion errors has attracted growing attention in recent literature. In this work, we further study this intriguing mathematical problem,…
Erasure list decoding was introduced to correct a larger number of erasures with output of a list of possible candidates. In the present paper, we consider both random linear codes and algebraic geometry codes for list decoding erasure…
This thesis makes several significant contributions to the theory of both Regenerating (RG) and Locally Recoverable (LR) codes. The two principal contributions are characterizing the optimal rate of an LR code designed to recover from $t$…
In this paper, we present a novel communication channel, called the absorption channel, inspired by information transmission in neurons. Our motivation comes from in-vivo nano-machines, emerging medical applications, and brain-machine…
In this paper, we construct systematic $q$-ary two-deletion correcting codes and burst-deletion correcting codes, where $q\geq 2$ is an even integer. For two-deletion codes, our construction has redundancy $5\log n+O(\log q\log\log n)$ and…
The problem of designing codes for deletion-correction and synchronization has received renewed interest due to applications in DNA-based data storage systems that use nanopore sequencers as readout platforms. In almost all instances,…
Burst errors involving simultaneous insertions, deletions, and substitutions occur in practical scenarios, including DNA data storage and document synchronization, motivating developments of channel codes that can correct such errors. In…
Cyclic redundancy check (CRC) codes check if a codeword is correctly received. This paper presents an algorithm to design CRC codes that are optimized for the code-specific error behavior of a specified feedforward convolutional code. The…
In 2009, a lossless compression algorithm based on 1D chaotic maps known as Generalized Lur\"{o}th Series (or GLS) has been proposed. This algorithm (GLS-coding) encodes the input message as a symbolic sequence on an appropriate 1D chaotic…
In this paper, we propose a partitioning technique that decomposes a pair of sequences with overlapping $t$-deletion $s$-substitution balls into sub-pairs, where the $^{\leq}t$-burst-deletion balls of each sub-pair intersect. This…
This paper investigates decoding of binary linear block codes over the binary erasure channel (BEC). Of the current iterative decoding algorithms on this channel, we review the Recovery Algorithm and the Guess Algorithm. We then present a…
In this paper, two moment balancing schemes, namely a variable index scheme and a fixed index scheme, for either single insertion/deletion error correction or multiple substitution error correction are introduced for coded sequences…
The sequence reconstruction problem, introduced by Levenshtein in 2001, considers a communication scenario where the sender transmits a codeword from some codebook and the receiver obtains multiple noisy reads of the codeword. Motivated by…
A new class of spatially-coupled turbo-like codes (SC-TCs), dubbed generalized spatially coupled parallel concatenated codes (GSC-PCCs), is introduced. These codes are constructed by applying spatial coupling on parallel concatenated codes…
We compare the performance of short-length linear binary codes on the binary erasure channel and the binary-input Gaussian channel. We use a universal decoder that can decode any linear binary block code: Gaussian-elimination based…
This paper constructs a non-binary code correcting a single $b$-burst of insertions or deletions with a large cardinality. This paper also proposes a decoding algorithm of this code and evaluates a lower bound of the cardinality of this…
The problem of correcting deletions has received significant attention, partly because of the prevalence of these errors in DNA data storage. In this paper, we study the problem of correcting a consecutive burst of at most $t$ deletions in…
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…