Related papers: Parallel multilevel constructions for constant dim…
We present a tree-based construction of LDPC codes that have minimum pseudocodeword weight equal to or almost equal to the minimum distance, and perform well with iterative decoding. The construction involves enumerating a $d$-regular tree…
Codes in the sum-rank metric have received many attentions in recent years, since they have wide applications in the multishot network coding, the space-time coding and the distributed storage. In this paper, by constructing covering codes…
We define linear and semilinear isometry for general subspace codes, used for random network coding. Furthermore, some results on isometry classes and automorphism groups of known constant dimension code constructions are derived.
In this paper, an expression for the asymptotic growth rate of the number of small linear-weight codewords of irregular doubly-generalized LDPC (D-GLDPC) codes is derived. The expression is compact and generalizes existing results for LDPC…
In this paper, an expression for the asymptotic growth rate of the number of small linear-weight codewords of irregular doubly-generalized LDPC (D-GLDPC) codes is derived. The expression is compact and generalizes existing results for LDPC…
In this paper, we present a new method for explicitly constructing regular low-density parity-check (LDPC) codes based on $\mathbb{S}_{n}(\mathbb{F}_{q})$, the space of $n\times n$ symmetric matrices over $\mathbb{F}_{q}$. Using this…
Ultra-reliable low-latency communication is essential in mission-critical settings, including military applications, where persistent and asymmetric link blockages caused by mobility, jamming, or adversarial attacks can disrupt…
Combinatorial Batch Codes (CBCs), replication-based variant of Batch Codes introduced by Ishai et al. in STOC 2004, abstracts the following data distribution problem: $n$ data items are to be replicated among $m$ servers in such a way that…
To better understand the wireless network design with a large number of hops, we investigate a line network formed by general discrete memoryless channels (DMCs), which may not be identical. Our focus lies on Generalized Batched Network…
We consider a special family of SC-LDPC codes, that is, time-invariant LDPCC codes, which are known in the literature for a long time. Codes of this kind are usually designed by starting from QC block codes, and applying suitable unwrapping…
We detail for the first time a complete explicit description of the quasi-cyclic structure of all classical finite generalized quadrangles. Using these descriptions we construct families of quasi-cyclic LDPC codes derived from the…
We investigate the minimum distance of structured binary Low-Density Parity-Check (LDPC) codes whose parity-check matrices are of the form $[\mathbf{C} \vert \mathbf{M}]$ where $\mathbf{C}$ is circulant and of column weight $2$, and…
Motivated by applications to the theory of rank-metric codes, we study the problem of estimating the number of common complements of a family of subspaces over a finite field in terms of the cardinality of the family and its intersection…
A new ensemble of structured codes is introduced. These codes are called Quasi Linear Codes (QLC). The QLC's are constructed by taking subsets of linear codes. They have a looser structure compared to linear codes and are not closed under…
Coded distributed computing (CDC) introduced by Li et. al. is an effective technique to trade computation load for communication load in a MapReduce framework. CDC achieves an optimal trade-off by duplicating map computations at $r$…
Lattice and special nonlattice multilevel constellations constructed from binary codes, such as Constructions A, C, and D, have relevant applications in Mathematics (sphere packing) and in Communication (multi-stage decoding and efficient…
In this paper, we consider the Reed-Muller (RM) codes. For the first order RM code, we prove that it is unique in the sense that any linear code with the same length, dimension and minimum distance must be the first order RM code; For the…
CC-GLPDC codes are a class of generalized low-density parity-check (GLDPC) codes where the constraint nodes (CNs) represent convolutional codes. This allows for efficient decoding in the trellis with the forward-backward algorithm, and the…
Let ${\cal G}$ be a family of graphs defined on a common (labeled) vertex set $V$. A set $S\subset V$ is said to be a simultaneous strong metric generator for ${\cal G}$ if it is a strong metric generator for every graph of the family. The…
In this work, we define Generalized Monomial Cartesian Codes (GMCC), which constitute a natural extension of generalized Reed-Solomon codes. We describe how two different generalized Reed-Solomon codes can be combined to construct one GMCC.…