Related papers: A Group Theoretic Construction of Batch Codes
We define a pseudo quasi-3 design as a symmetric design with the property that the derived and residual designs with respect to at least one block are quasi-symmetric. Quasi-symmetric designs can be used to construct optimal self…
Low-rate and short-packet transmissions are important for ultra-reliable low-latency communications (URLLC). In this paper, we put forth a new family of sparse superposition codes for URLLC, called block orthogonal sparse superposition…
Perfect codes are arguably the most fascinating structures in combinatorial coding theory, and their classification and weight distribution are of considerable interest. This classification also involves the analysis of some related…
Low check weight is practically crucial code property for fault-tolerant quantum computing, which underlies the strong interest in quantum low-density parity-check (qLDPC) codes. Here, we explore the theory of weight-constrained stabilizer…
Ever-increasing amounts of data are created and processed in internet-scale companies such as Google, Facebook, and Amazon. The efficient storage of such copious amounts of data has thus become a fundamental and acute problem in modern…
In recent years, locally repairable codes (LRCs) have attracted considerable attention owing to their pivotal role in distributed storage systems. Since binary linear locally repairable codes can significantly reduce the complexity of both…
This is a manuscript of a chapter prepared for a book. The good codes possess large information length and large minimum distance. A class of codes is said to be asymptotically good if there exists a positive real $\delta$ such that, for…
Due to their efficient encoding and decoding algorithms cyclic codes, a subclass of linear codes, have applications in consumer electronics, data storage systems, and communication systems. In this paper, Dickson polynomials of the first…
We consider the problem of coded distributed computing where a large linear computational job, such as a matrix multiplication, is divided into $k$ smaller tasks, encoded using an $(n,k)$ linear code, and performed over $n$ distributed…
LT codes and digital fountain techniques have received significant attention from both academics and industry in the past few years. There have also been extensive interests in applying LT code techniques to distributed storage systems such…
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. Fundamental bounds, some explicit or…
It is well known that quantum codes can be constructed by means of classical symplectic dual-containing codes. This paper considers a family of two-generator quasi-cyclic codes and derives sufficient conditions for these codes to be…
In this short review, I draw attention to new developments in the theory of fault tolerance in quantum computation that may give concrete direction to future work in the development of superconducting qubit systems. The basics of quantum…
Information theoretic analysis of a coded caching system is considered, in which a server with a database of N equal-size files, each F bits long, serves K users. Each user is assumed to have a local cache that can store M files, i.e.,…
In a distributed space-time coding scheme, based on the relay channel model, the relay nodes co-operate to linearly process the transmitted signal from the source and forward them to the destination such that the signal at the destination…
Fault-tolerant quantum computation critically depends on architectures uniting high encoding rates with physical implementability. Quantum low-density parity-check (qLDPC) codes, including bivariate bicycle (BB) codes, achieve dramatic…
This paper introduces a novel framework for constructing algebraic lattices based on Construction-D, leveraging nested linear codes and prime ideals from algebraic number fields. We focus on the application of these lattices in block-fading…
A simple and general definition of quasi cyclic low density parity check (QC LDPC) codes which are constructed based on circulant permutation matrices (CPM) is proposed. As an special case of this definition, we first represent one type of…
Chase-like decoding algorithms are a popular choice for soft-input decoding of algebraic codes. In this paper, we evaluate the performance of different test pattern sets using three methods. For test pattern sets with a certain structure…
An elementary combinatorial Tanner graph construction for a family of near-regular low density parity check codes achieving high girth is presented. The construction allows flexibility in the choice of design parameters like rate, average…