Related papers: Parallel Concatenation of Non-Binary Linear Random…
This paper considers the joint-decoding (JD) problem for finite-state channels (FSCs) and low-density parity-check (LDPC) codes. In the first part, the linear-programming (LP) decoder for binary linear codes is extended to JD of…
Fountain codes are becoming increasingly important for data transferring over dedicated high-speed long-distance network. However, the encoding and decoding complexity of traditional fountain codes such as LT and Raptor codes are still…
This work presents a theoretical analysis of the probability of successfully retrieving data encoded with MDS codes (e.g., Reed-Solomon codes) in DNA storage systems. We study this probability under independent and identically distributed…
A collection of sets satisfies a $(\delta,\varepsilon)$-proximity gap with respect to some property if for every set in the collection, either (i) all members of the set are $\delta$-close to the property in (relative) Hamming distance, or…
In this paper, we propose a methodology to compute the optimal finite-length coding rate for random linear network coding schemes over a line network. To do so, we first model the encoding, reencoding, and decoding process of different…
When binary linear error-correcting codes are used over symmetric channels, a relaxed version of the maximum likelihood decoding problem can be stated as a linear program (LP). This LP decoder can be used to decode error-correcting codes at…
This paper studies decentralized, Fountain and network-coding based strategies for facilitating data collection in circular wireless sensor networks, which rely on the stochastic diversity of data storage. The goal is to allow for a reduced…
In this paper we consider a Metzner-Kapturowski-like decoding algorithm for high-order interleaved sum-rank-metric codes, offering a novel perspective on the decoding process through the concept of an error code. The error code, defined as…
Self-dual maximum distance separable codes (self-dual MDS codes) and self-dual near MDS codes are very important in coding theory and practice. Thus, it is interesting to construct self-dual MDS or self-dual near MDS codes. In this paper,…
Network-coded multiple access (NCMA) is a communication scheme for wireless multiple-access networks where physical-layer network coding (PNC) is employed. In NCMA, a user encodes and spreads its message into multiple packets. Time is…
In this paper we survey the various erasure codes which had been proposed and patented recently, and along the survey we provide introductory tutorial on many of the essential concepts and readings in erasure and Fountain codes. Packet…
In this paper, we present a new family of fountain codes which overcome adversarial errors. That is, we consider the possibility that some portion of the arriving packets of a rateless erasure code are corrupted in an undetectable fashion.…
We consider decoding of binary Tanner codes using message-passing iterative decoding and linear programming (LP) decoding in MBIOS channels. We present new certificates that are based on a combinatorial characterization for local-optimality…
Two of the most common models for channels with synchronisation errors are the Binary Deletion Channel with parameter $p$ ($\text{BDC}_p$) -- a channel where every bit of the codeword is deleted i.i.d with probability $p$, and the Poisson…
Two concatenated coding schemes based on fixed-rate Raptor codes are proposed for error control in NAND flash memory. One is geared for off-line recovery of uncorrectable pages and the other is designed for page error correction during the…
In this paper we study the problem of increasing the decoding success probability of random linear fountain code over GF(2) for small packet lengths used in delay-intolerant applications such as multimedia streaming. Such code over GF(2)…
This paper is focused on the performance analysis of binary linear block codes (or ensembles) whose transmission takes place over independent and memoryless parallel channels. New upper bounds on the maximum-likelihood (ML) decoding error…
The recent development of deep learning methods provides a new approach to optimize the belief propagation (BP) decoding of linear codes. However, the limitation of existing works is that the scale of neural networks increases rapidly with…
Motivated by recent developments in coding theory, particular in list-decoding, we introduce a new error model which we call semi-adversarial errors. This error model bridges between fully random errors and fully adversarial errors by…
A scheme for concatenating the recently invented polar codes with interleaved block codes is considered. By concatenating binary polar codes with interleaved Reed-Solomon codes, we prove that the proposed concatenation scheme captures the…