Related papers: Simultaneous Rational Function Codes: Improved Ana…
We extend Robust Optimization to fractional programming, where both the objective and the constraints contain uncertain parameters. Earlier work did not consider uncertainty in both the objective and the constraints, or did not use Robust…
In this paper we study some iterative methods for simultaneous approximation of polynomial zeros. We give new semilocal convergence theorems with error bounds for Ehrlich's and Nourein's iterations. Our theorems generalize and improve…
In this work, we present hardware and software implementations of flexible polar systematic encoders and decoders. The proposed implementations operate on polar codes of any length less than a maximum and of any rate. We describe the…
We present a new rational approximation algorithm based on the empirical interpolation method for interpolating a family of parametrized functions to rational polynomials with invariant poles, leading to efficient numerical algorithms for…
Recently, codes in the sum-rank metric attracted attention due to several applications in e.g. multishot network coding, distributed storage and quantum-resistant cryptography. The sum-rank analogs of Reed-Solomon and Gabidulin codes are…
We consider hard-decision iterative decoders for product codes over the erasure channel, which employ repeated rounds of decoding rows and columns alternatingly. We derive the exact asymptotic probability of decoding failure as a function…
A scheme for concatenating the recently invented polar codes with non-binary MDS codes, as Reed-Solomon codes, is considered. By concatenating binary polar codes with interleaved Reed-Solomon codes, we prove that the proposed concatenation…
Cooperative optimization is a new way for finding global optima of complicated functions of many variables. It has some important properties not possessed by any conventional optimization methods. It has been successfully applied in solving…
The applications of the partial fraction decomposition in control and systems engineering are several. In this letter, we propose a new interpretation of residues in the partial fraction decomposition, which is employed for the following…
This paper investigates the error probability of several decoding methods for a source code with decoder side information, where the decoding methods are: 1) symbol-wise maximum a posteriori decoding, 2) successive-cancellation decoding,…
Using linear functional-based duality of modules, we generalize the syndrome decoding algorithm of linear codes over finite fields to those over finite commutative rings. Moreover, If the ring is local the algorithm is simplified by…
In this paper, we study polar codes from a practical point of view. In particular, we study concatenated polar codes and rate-compatible polar codes. First, we propose a concatenation scheme including polar codes and Low-Density…
A scheme for concatenating the recently invented polar codes with interleaved block codes is considered. By concatenating binary polar codes with interleaved Reed-Solomon codes, we prove that the proposed concatenation scheme captures the…
Many probabilistic inference tasks involve summations over exponentially large sets. Recently, it has been shown that these problems can be reduced to solving a polynomial number of MAP inference queries for a model augmented with randomly…
Motivated by a use case in theoretical hadron physics, we revisit an application of a pole-sum fit to dressing functions of a confined quark propagator. More precisely, we investigate approaches to determine the number and positions of the…
General computational methods based on descriptor state-space realizations are proposed to compute coprime factorizations of rational matrices with minimum degree denominators. The new methods rely on recursive pole dislocation techniques,…
The extended L\"uroth's Theorem says that if the transcendence degree of $\KK(\mathsf{f}_1,\dots,\mathsf{f}_m)/\KK$ is 1 then there exists $f \in \KK(\underline{X})$ such that $\KK(\mathsf{f}_1,\dots,\mathsf{f}_m)$ is equal to $\KK(f)$. In…
Polar codes are a new class of capacity-achieving error-correcting codes with low encoding and decoding complexity. Their low-complexity decoding algorithms rendering them attractive for use in software-defined radio applications where…
Recent years have witnessed the introduction and development of extremely fast rational function algorithms. Many ideas in this realm arose from polynomial-based linear-algebraic algorithms. However, polynomial approximation is occasionally…
B\o gvad and H\"agg proved that for a rational function with simple poles, the zeros of successive derivatives accumulate on the Voronoi diagram of the pole set, and the normalized zero-counting measures converge to a canonical probability…