Related papers: Strange Attractor for Efficient Polar Code Design
Classical block designs are important combinatorial structures with a wide range of applications in Computer Science and Statistics. Here we give a new abstract description of block designs based on the arrow category construction. We show…
In this work, we investigate the simultaneous goodness of polar codes and polar lattices. The simultaneous goodness of a lattice or a code means that it is optimal for both channel coding and source coding simultaneously. The existence of…
Polar coding over a class of binary discrete memoryless channels with channel knowledge at the encoder is studied. It is shown that polar codes achieve the capacity of convex and one-sided classes of symmetric channels.
The additive codes may have better parameters than linear codes. However, it is still a challenging problem to efficiently construct additive codes that outperform linear codes, especially those with greater distances than linear codes of…
An archetypal problem discussed in computer science is the problem of searching for a given number in a given set of numbers. Other than sequential search, the classic solution is to sort the list of numbers and then apply binary search.…
Monads can be interpreted as encoding formal expressions, or formal operations in the sense of universal algebra. We give a construction which formalizes the idea of "evaluating an expression partially": for example, "2+3" can be obtained…
Despite their apparent simplicity, random Boolean networks display a rich variety of dynamical behaviors. Much work has been focused on the properties and abundance of attractors. We here derive an expression for the number of attractors in…
We prove the existence of a global random attractor for a certain class of stochastic partly dissipative systems. These systems consist of a partial (PDE) and an ordinary differential equation (ODE), where both equations are coupled and…
In this paper, we introduce a new coding and decoding structure for enhancing the reliability and performance of polar codes, specifically at low error rates. We achieve this by concatenating two polar codes in series to create robust…
The article focuses on word (or string) attractors, which are sets of positions related to the text compression efficiency of the underlying word. The article presents two combinatorial algorithms based on Suffix automata or Directed…
We put forth new models for universal channel coding. Unlike standard codes which are designed for a specific type of channel, our most general universal code makes communication resilient on every channel, provided the noise level is below…
A general framework is proposed that includes polar codes over arbitrary channels with arbitrary kernels. The asymptotic tradeoff among block length $N$, code rate $R$, and error probability $P$ is analyzed. Given a tradeoff between $N,P$…
In this paper, we propose a new polar code construction by employing kernels of different sizes in the Kronecker product of the transformation matrix, thus generalizing the original construction by Arikan. The proposed multi-kernel polar…
A list decoding scheme for universal polar codes is presented. Our scheme applies to the universal polar codes first introduced by Sasoglu and Wang, and generalized to processes with memory by the authors. These codes are based on the…
In this paper, we investigate the fundamentals of puncturing and shortening for polar codes, based on binary domination which plays a key role in polar code construction. We first prove that the orders of encoder input bits to be made…
Well-partial orders, and the ordinal invariants used to measure them, are relevant in set theory, program verification, proof theory and many other areas of computer science and mathematics. In this article we focus on one of the most…
We introduce a new family of polar-like codes, called Partially Polarized Polar (PPP) codes. PPP codes are constructed from conventional polar codes by selectively pruning polarization kernels, thereby modifying the synthesized bit-channel…
In this paper, we first establish a criterion based on contractive function for the existence of polynomial attractors. This criterion only involves some rather weak compactness associated with the repeated limit inferior and requires no…
The exponential ordering is exploited in the context of non-auto\-no\-mous delay systems, inducing monotone skew-product semiflows under less restrictive conditions than usual. Some dynamical concepts linked to the order, such as…
This paper presents the first proof of polarization for the deletion channel with a constant deletion rate and a regular hidden-Markov input distribution. A key part of this work involves representing the deletion channel using a trellis…