Related papers: Augmented space recursion code and application in …
This paper presents several new construction techniques for low-density parity-check (LDPC) and systematic repeat-accumulate (RA) codes. Based on specific classes of combinatorial designs, the improved code design focuses on high-rate…
We introduce alphabet-permutation (AP) codes, a new family of error-correcting codes defined by iteratively applying random coordinate-wise permutations to a fixed initial word. A special case recovers random additive codes and random…
Augmented designs are typically used in early-stage breeding programs to compare single replicates of test entries by combining them with replicated check varieties. One or two dimensional incomplete blocking can be incorporated in the…
Linear Complementary Dual codes (LCD) are binary linear codes that meet their dual trivially. We construct LCD codes using orthogonal matrices, self-dual codes, combinatorial designs and Gray map from codes over the family of rings $R_k$.…
Hinging on ideas from physical-layer network coding, some promising proposals of coded random access systems seek to improve system performance (while preserving low complexity) by means of packet repetitions and decoding of linear…
Lifted Reed Solomon Codes (Guo, Kopparty, Sudan 2013) were introduced in the context of locally correctable and testable codes. They are multivariate polynomials whose restriction to any line is a codeword of a Reed-Solomon code. We…
Lifted Reed-Solomon codes and multiplicity codes are two classes of evaluation codes that allow for the design of high-rate codes that can recover every codeword or information symbol from many disjoint sets. Recently, the underlying…
Optimal recursive decomposition (or DR-planning) is crucial for analyzing, designing, solving or finding realizations of geometric constraint sytems. While the optimal DR-planning problem is NP-hard even for general 2D bar-joint constraint…
Quantum synchronizable codes are quantum error-correcting codes that can correct the effects of quantum noise as well as block synchronization errors. We improve the previously known general framework for designing quantum synchronizable…
Two concatenated coding schemes incorporating algebraic Reed-Solomon (RS) codes and polarization-adjusted convolutional (PAC) codes are proposed. Simulation results show that at a bit error rate of $10^{-5}$, a concatenated scheme using RS…
In recent work we have shown how an accurate reduced model can be utilized to perform mesh refinement in random space. That work relied on the explicit knowledge of an accurate reduced model which is used to monitor the transfer of activity…
To facilitate rational molecular and materials design, this research proposes an integrated computational framework that combines stochastic simulation, ab initio quantum chemistry, and molecular docking. The suggested workflow allows…
We have carried out numerical simulations of strongly gravitating systems based on the Einstein equations coupled to the relativistic hydrodynamic equations using adaptive mesh refinement (AMR) techniques. We show AMR simulations of NS…
A general method of coding over expansions is proposed, which allows one to reduce the highly non-trivial problem of coding over continuous channels to a much simpler discrete ones. More specifically, the focus is on the additive…
Error-correcting codes are usually envisioned to counter errors by operating unitary corrections depending on the projective measurement results of some syndrome observables. We here propose a way to use them in a more integrated way, where…
As we rapidly approach the frontiers of ultra large computing resources, software optimization is becoming of paramount interest to scientific application developers interested in efficiently leveraging all available on-Node computing…
Extended formulations are an important tool in polyhedral combinatorics. Many combinatorial optimization problems require an exponential number of inequalities when modeled as a linear program in the natural space of variables. However, by…
Considerable interest has been paid in recent literature to codes combining local and global properties for erasure correction. Applications are in cloud type of implementations, in which fast recovery of a failed storage device is…
This work shows several direct and recursive constructions of ordered covering arrays using projection, fusion, column augmentation, derivation, concatenation and cartesian product. Upper bounds on covering codes in NRT spaces are also…
Holographic quantum error-correcting code, the quantum-information structure hypothesized for the AdS/CFT correspondence, has being attracting increasing attention in new directions interrelating the studies of quantum gravity and quantum…