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Determining the achievable rate region for networks using routing, linear coding, or non-linear coding is thought to be a difficult task in general, and few are known. We describe the achievable rate regions for four interesting networks…
An index code is said to be locally decodable if each receiver can decode its demand using its side information and by querying only a subset of the transmitted codeword symbols instead of observing the entire codeword. Local decodability…
This paper concerns itself with the question of list decoding for general adversarial channels, e.g., bit-flip ($\textsf{XOR}$) channels, erasure channels, $\textsf{AND}$ ($Z$-) channels, $\textsf{OR}$ channels, real adder channels, noisy…
Low-Density Parity-Check (LDPC) codes received much attention recently due to their capacity-approaching performance. The iterative message-passing algorithm is a widely adopted decoding algorithm for LDPC codes \cite{Kschischang01}. An…
We present a coded caching framework using line graphs of bipartite graphs. A clique cover of the line graph describes the uncached subfiles at users. A clique cover of the complement of the square of the line graph gives a transmission…
Protograph low-density-parity-check (LDPC) are considered to design near-capacity low-rate codes over the binary erasure channel (BEC) and binary additive white Gaussian noise (BIAWGN) channel. For protographs with degree-one variable nodes…
The service rate region of a coded distributed storage system is the set of all achievable data access requests under the capacity constraints. This paper investigates the service rate regions of systematic Hamming codes using hypergraph…
Due to the short and bursty incoming messages, channel access activities in a wireless random access system are often fractional. The lack of frequent data support consequently makes it difficult for the receiver to estimate and track the…
We solve the problem of designing powerful low-density parity-check (LDPC) codes with iterative decoding for the block-fading channel. We first study the case of maximum-likelihood decoding, and show that the design criterion is rather…
The non-binary low-density parity-check (NB-LDPC) codes can offer promising performance advantages but suffer from high decoding complexity. To tackle this challenge, in this paper, we consider NB-LDPC codes over finite fields as codes over…
An $r$-identifying code on a graph $G$ is a set $C\subset V(G)$ such that for every vertex in $V(G)$, the intersection of the radius-$r$ closed neighborhood with $C$ is nonempty and unique. On a finite graph, the density of a code is…
A class of linear block codes which simultaneously generalizes Gabidulin codes and a class of skew cyclic codes is defined. For these codes, both a Hartmann-Tzeng-like bound and a Roos-like bound, with respect to their rank distance, are…
We discuss and analyze a list-message-passing decoder with verification for low-density parity-check (LDPC) codes on the q-ary symmetric channel (q-SC). Rather than passing messages consisting of symbol probabilities, this decoder passes…
We propose a novel technique for constructing a graph representation of a code through which we establish a significant connection between the service rate problem and the well-known fractional matching problem. Using this connection, we…
Consider an assignment of bits to the vertices of a connected graph $G(V,E)$ with the property that the value of each vertex is a function of the values of its neighbors. A collection of such assignments is called a {\em storage code} of…
We consider communication over memoryless channels using low-density parity-check code ensembles above the iterative (belief propagation) threshold. What is the computational complexity of decoding (i.e., of reconstructing all the typical…
Achievable and converse bounds for general channels and mismatched decoding are derived. The direct (achievable) bound is derived using random coding and the analysis is tight up to factor 2. The converse is given in term of the achievable…
This paper presents general bounds on the highest achievable rate for list-decodable insertion-deletion codes. In particular, we give novel outer and inner bounds for the highest achievable communication rate of any insertion-deletion code…
A set of linearly constrained permutation matrices are proposed for constructing a class of permutation codes. Making use of linear constraints imposed on the permutation matrices, we can formulate a minimum Euclidian distance decoding…
The asymptotic iterative decoding performances of low-density parity-check (LDPC) codes using min-sum (MS) and sum-product (SP) decoding algorithms on memoryless binary-input output-symmetric (MBIOS) channels are analyzed in this paper. For…