Related papers: Pseudo-MDP Convolutional Codes for Burst Erasure C…
We study the construction of $d$-deletion-correcting binary codes by formulating the problem as a Maximum Clique Problem (MCP). In this formulation, vertices represent candidate codewords and edges connect pairs whose longest common…
It is well known that spatially coupled (SC) codes with erasure-BP decoding have powerful error correcting capability over memoryless erasure channels. However, the decoding performance of SC-codes significantly degrades when they are used…
We construct a family of (n,k) convolutional codes with degree \delta in {k,n-k} that have a maximum distance profile. The field size required for our construction is of the order n^{2\delta}, which improves upon the known constructions of…
Classical multidimensional scaling only works well when the noisy distances observed in a high dimensional space can be faithfully represented by Euclidean distances in a low dimensional space. Advanced models such as Maximum Variance…
In this paper, for the purposes of information transmission and network error correction simultaneously, three classes of important linear network codes in network coding, linear multicast/broadcast/dispersion codes are generalized to…
In this paper, we first introduce the concept of elementary linear subspace, which has similar properties to those of a set of coordinates. We then use elementary linear subspaces to derive properties of maximum rank distance (MRD) codes…
We derive Singleton-type bounds on the free distance and column distances of trellis codes. Our results show that, at a given time instant, the maximum attainable column distance of trellis codes can exceed that of convolutional codes.…
We consider error decoding of locally repairable codes (LRC) and partial MDS (PMDS) codes through interleaved decoding. For a specific class of LRCs we investigate the success probability of interleaved decoding. For PMDS codes we show that…
In this paper, we construct new families of convolutional codes. Such codes are obtained by means of algebraic geometry codes. Additionally, more families of convolutional codes are constructed by means of puncturing, extending, expanding…
This paper proposes a novel maximum-likelihood (ML) soft-decision decoding framework for linear block codes, termed error-building decoding (EBD). The complete decoding process can be performed using only the parity-check matrix, without…
In diffusion based molecular communication, the intersymbol interference (ISI) is an important reason for system performance degradation, which is caused by the random movement, out-of-order arrival and indistinguishability of the…
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…
Fractional repetition (FR) codes are a class of repair efficient erasure codes that can recover a failed storage node with both optimal repair bandwidth and complexity. In this paper, we study the minimum distance of FR codes, which is the…
In this paper we study function-correcting codes, a new class of codes designed to protect the function evaluation of a message against errors. We show that FCCs are equivalent to irregular-distance codes, i.e., codes that obey some given…
A new class of exact-repair regenerating codes is constructed by stitching together shorter erasure correction codes, where the stitching pattern can be viewed as block designs. The proposed codes have the "help-by-transfer" property where…
We consider a windowed decoding scheme for LDPC convolutional codes that is based on the belief-propagation (BP) algorithm. We discuss the advantages of this decoding scheme and identify certain characteristics of LDPC convolutional code…
Optimal locally repairable codes with information locality are considered. Optimal codes are constructed, whose length is also order-optimal with respect to a new bound on the code length derived in this paper. The length of the constructed…
We introduce a new approach to proving that a sequence of deterministic linear codes achieves capacity on an erasure channel under maximum a posteriori decoding. Rather than relying on the precise structure of the codes our method exploits…
We define a new class of Convolutional Codes in terms of fibrations of algebraic varieties generalizaing our previous constructions of Convolutional Goppa Codes. Using this general construction we can give several examples of Maximum…
Maximum distance separable (MDS) array codes constitute an important class of error-correcting codes due to their optimal distance properties and their relevance in distributed storage systems. In this paper, we investigate the construction…