Related papers: Two Deletion Correcting Codes from Indicator Vecto…
Error exponents characterize the exponential decay, when increasing message length, of the probability of error of many error-correcting codes. To tackle the long standing problem of computing them exactly, we introduce a general,…
Function-correcting codes are a class of codes designed to protect the function evaluation of a message against errors whose key advantage is the reduced redundancy. In this paper, we extend function-correcting codes from binary symmetric…
Owing to its several merits over other DNA sequencing technologies, nanopore sequencers hold an immense potential to revolutionize the efficiency of DNA storage systems. However, their higher error rates necessitate further research to…
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…
Consider binary linear codes obtained from bipartite graphs as follows. There are~\(k \geq 1\) left nodes each representing a message bit and there are~\(m = m(k)\) right nodes each representing a parity bit, generated from the…
This paper presents a coding scheme for an insertion deletion substitution channel. We extend a previous scheme for the deletion channel where polar codes are modified by adding "guard bands" between segments. In the new scheme, each guard…
The rapidly improving performance of modern hardware renders convolutional codes obsolete, and allows for the practical implementation of more sophisticated correction codes such as low density parity check (LDPC) and turbo codes (TC). Both…
For an arbitrary degree distribution pair (DDP), we construct a sequence of low-density parity-check (LDPC) code ensembles with girth growing logarithmically in block-length using Ramanujan graphs. When the DDP has minimum left degree at…
We propose a new low-density parity-check code construction scheme based on 2-lifts. The proposed codes have an advantage of admitting efficient hardware implementations. With the motivation of designing codes with low error floors, we…
In this letter, we present a hybrid iterative decoder for non-binary low density parity check (LDPC) codes over binary erasure channel (BEC), based on which the recursion of the erasure probability is derived to design non-binary LDPC codes…
The analysis of the decoding failure rate of the bit-flipping algorithm has received increasing attention. For a binary linear code we consider the minimum number of rows in a parity-check matrix such that the bit-flipping algorithm is able…
This paper considers a base station that delivers packets to multiple receivers through a sequence of coded transmissions. All receivers overhear the same transmissions. Each receiver may already have some of the packets as side…
Due to their weak algebraic structure, low rank parity check (LRPC) codes have been employed in several post-quantum cryptographic schemes. In this paper we propose new improved decoding algorithms for (n, k) LRPC codes of dual rank weight…
We consider transmission over a binary-input additive white Gaussian noise channel using low-density parity-check codes. One of the most popular techniques for decoding low-density parity-check codes is the linear programming decoder. In…
In distributed storage systems that employ erasure coding, the issue of minimizing the total {\it communication} required to exactly rebuild a storage node after a failure arises. This repair bandwidth depends on the structure of the…
This paper studies the cardinality of codes correcting insertions and deletions. We give improved upper and lower bounds on code size. Our upper bound is obtained by utilizing the asymmetric property of list decoding for insertions and…
Analysis of the Berlekamp-Massey-Sakata algorithm for decoding one-point codes leads to two methods for improving code rate. One method, due to Feng and Rao, removes parity checks that may be recovered by their majority voting algorithm.…
One of the main challenges in developing racetrack memory systems is the limited precision in controlling the track shifts, that in turn affects the reliability of reading and writing the data. A current proposal for combating deletions in…
A new deep-neural-network (DNN) based error correction encoder architecture for channels with feedback, called Deep Extended Feedback (DEF), is presented in this paper. The encoder in the DEF architecture transmits an information message…
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…