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"Extended Clifford algebras" are introduced as a means to obtain low ML decoding complexity space-time block codes. Using left regular matrix representations of two specific classes of extended Clifford algebras, two systematic algebraic…
Lattices and partially ordered sets have played an increasingly important role in coding theory, providing combinatorial frameworks for studying structural and algebraic properties of error-correcting codes. Motivated by recent works…
We approximate $d$-variate periodic functions in weighted Korobov spaces with general weight parameters using $n$ function values at lattice points. We do not limit $n$ to be a prime number, as in currently available literature, but allow…
Variable-length splittable codes are derived from encoding sequences of ordered integer pairs, where one of the pair's components is upper bounded by some constant, and the other one is any positive integer. Each pair is encoded by the…
This paper investigates the structure-property relations of thin-walled lattices under dynamic longitudinal compression, characterized by their cross-sections and heights. These relations elucidate the interactions of different geometric…
Most practical constructions of lattice codes with high coding gains are multilevel constructions where each level corresponds to an underlying code component. Construction D, Construction D$'$, and Forney's code formula are classical…
There are deep, but hidden, geometric structures within jammed systems, associated with hidden symmetries. These can be revealed by repeated transformations under which these structures lead to fixed points. These geometric structures can…
Coding for distributed computing supports low-latency computation by relieving the burden of straggling workers. While most existing works assume a simple master-worker model, we consider a hierarchical computational structure consisting of…
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…
Quantum low-density parity-check (QLDPC) codes offer a promising route to scalable fault-tolerant quantum computation, but their performance under iterative decoding is strongly influenced by short-cycle structure and other harmful…
Non-binary low-density parity-check codes are robust to various channel impairments. However, based on the existing decoding algorithms, the decoder implementations are expensive because of their excessive computational complexity and…
We introduce a new class of algorithms for finding a short vector in lattices defined by codes of co-dimension $k$ over $\mathbb{Z}_P^d$, where $P$ is prime. The co-dimension $1$ case is solved by exploiting the packing properties of the…
We use random linear network coding (RLNC) based scheme for multipath communication in the presence of lossy links with different delay characteristics to obtain ultra-reliability and low latency. A sliding window version of RLNC is…
Although digital fabrication processes at the desktop scale have become proficient and prolific, systems aimed at producing larger-scale structures are still typically complex, expensive, and unreliable. In this work, we present an approach…
A recent line of work on lattice codes for Gaussian wiretap channels introduced a new lattice invariant called secrecy gain as a code design criterion which captures the confusion that lattice coding produces at an eavesdropper. Following…
In a seminal work, Micciancio & Voulgaris (2013) described a deterministic single-exponential time algorithm for the Closest Vector Problem (CVP) on lattices. It is based on the computation of the Voronoi cell of the given lattice and thus…
Voronoi diagrams appear in many areas in science and technology and have numerous applications. They have been the subject of extensive investigation during the last decades. Roughly speaking, they are a certain decomposition of a given…
Distributed storage systems suffer from significant repair traffic generated due to frequent storage node failures. This paper shows that properly designed low-density parity-check (LDPC) codes can substantially reduce the amount of…
The linear error-correcting codes are known to be well suited for battling and correcting the burst errors caused by noise in the wireless data transmission system. However, different types of codes offer different decoding and…
Codes constructed from connected spatially coupled low-density parity-check code (SC-LDPCC) chains are proposed and analyzed. It is demonstrated that connecting coupled chains results in improved iterative decoding performance. The…