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A new type of spatially coupled low-density parity-check (SC-LDPC) codes motivated by practical storage applications is presented. SC-LDPCL codes (suffix 'L' stands for locality) can be decoded locally at the level of sub-blocks that are…
Multiply constant-weight codes (MCWCs) have been recently studied to improve the reliability of certain physically unclonable function response. In this paper, we give combinatorial constructions for MCWCs which yield several new infinite…
In this paper, we deal with time-invariant spatially coupled low-density parity-check convolutional codes (SC-LDPC-CCs). Classic design approaches usually start from quasi-cyclic low-density parity-check (QC-LDPC) block codes and exploit…
We generalize staircase codes and tiled diagonal zipper codes, preserving their key properties while allowing each coded symbol to be protected by arbitrarily many component codewords rather than only two. This generalization which we term…
The dimension of a linear space is the maximum positive integer $d$ such that any $d$ of its points generate a proper subspace. For a set $K$ of integers at least two, recall that a pairwise balanced design PBD$(v,K)$ is a linear space on…
Coding theoretic approached have been developed to significantly reduce the communication load in modern distributed computing system. In particular, coded distributed computing (CDC) introduced by Li et al. can efficiently trade…
This letter proposes a direct construction for cross Z-complementary sets (CZCSs) with flexible lengths and a large zero correlation zone (ZCZ). CZCS is an extension of the cross Z-complementary pair (CZCP). The maximum possible ZCZ width…
In this paper, we construct protograph-based spatially coupled low-density parity-check (SC-LDPC) codes by coupling together a series of L disjoint, or uncoupled, LDPC code Tanner graphs into a single coupled chain. By varying L, we obtain…
In this paper, we analyze the finite-length performance of codes on graphs constructed by connecting spatially coupled low-density parity-check (SC-LDPC) code chains. Successive (peeling) decoding is considered for the binary erasure…
Coded distributed computing (CDC) introduced by Li et al. in 2015 offers an efficient approach to trade computing power to reduce the communication load in general distributed computing frameworks such as MapReduce. For the more general…
Finding meaningful communities - subnetworks of interest within a large scale network - is a problem with a variety of applications. Most existing work towards community detection focuses on a single network. However, many real-life…
In this article, constant dimension subspace codes whose codewords have subspace distance in a prescribed set of integers, are considered. The easiest example of such an object is a {\it junta}; i.e. a subspace code in which all codewords…
Cycles and Cliques in a side-information graph reduce the number of transmissions required in an index coding problem. Thapa, Ong and Johnson defined a more general form of overlapping cycles, called the interlinked-cycle (IC) structure,…
A $(k,k-t)$-SCID (set of Subspaces with Constant Intersection Dimension) is a set of $k$-dimensional vector spaces that have pairwise intersections of dimension $k-t$. Let $\mathcal{C}=\{\pi_1,\ldots,\pi_n\}$ be a $(k,k-t)$-SCID. Define…
In this work, we propose and analyze a generalized construction of distributed network codes for a network consisting of $M$ users sending different information to a common base station through independent block fading channels. The aim is…
SC-LDPC codes with sub-block locality can be decoded locally at the level of sub-blocks that are much smaller than the full code block, thus providing fast access to the coded information. The same code can also be decoded globally using…
Generalized low-density parity-check (GLDPC) codes, where single parity-check constraints on the code bits are replaced with generalized constraints (an arbitrary linear code), are a promising class of codes for low-latency communication.…
Linear complementary dual (LCD) codes are linear codes which intersect their dual codes trivially, which have been of interest and extensively studied due to their practical applications in computational complexity and information…
We investigate graphs that have characteristic-dependent well-covered dimension and show how more of these graphs can be constructed from known ones.
A generalized low-density parity-check (GLDPC) code is a class of codes, where single parity check nodes in a conventional low-density parity-check (LDPC) code are replaced by linear codes with higher parity check constraints. In this…