Related papers: Polar Grassmannians and their Codes
Polar codes form a very powerful family of codes with a low complexity decoding algorithm that attain many information theoretic limits in error correction and source coding. These codes are closely related to Reed-Muller codes because both…
Codes in the Grassmannian have recently found an application in random network coding. All the codewords in such codes are subspaces of $\F_q^n$ with a given dimension. In this paper, we consider the problem of list decoding of a certain…
This paper is a short introduction to orthogonal polynomials, both the general theory and some special classes. It ends with some remarks about the usage of computer algebra for this theory.
Polar codes are widely used in modern communication systems due to their capacity-achieving properties. This paper investigates the importance of coded bits in the decoding process of polar codes and aims to determine which bits contribute…
Product codes are widespread in optical communications, thanks to their high throughput and good error-correction performance. Systematic polar codes have been recently considered as component codes for product codes. In this paper, we…
We propose an alternative method for collaborative decoding of interleaved Reed-Solomon codes. Simulation results for a concatenated coding scheme using polar codes as inner codes are included.
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…
List decoding of Hermitian codes is reformulated to allow an efficient and simple algorithm for the interpolation step. The algorithm is developed using the theory of Groebner bases of modules. The computational complexity of the algorithm…
The Grassmann manifold of linear subspaces is important for the mathematical modelling of a multitude of applications, ranging from problems in machine learning, computer vision and image processing to low-rank matrix optimization problems,…
The recently-discovered polar codes are widely seen as a major breakthrough in coding theory. These codes achieve the capacity of many important channels under successive cancellation decoding. Motivated by the rapid progress in the theory…
Codes in the Grassmannian space have found recently application in network coding. Representation of $k$-dimensional subspaces of $\F_q^n$ has generally an essential role in solving coding problems in the Grassmannian, and in particular in…
We characterize the range of the cosine transform on real Grassmannians in terms of the decomposition under the action of the special orthogonal group SO(n). Also a geometric interpretation of its image is given. The non- Archimedean…
Polar codes are a recently proposed family of provably capacity-achieving error-correction codes that received a lot of attention. While their theoretical properties render them interesting, their practicality compared to other types of…
Cyclic orbit codes are a family of constant dimension codes used for random network coding. We investigate the Pl\"ucker embedding of these codes and show how to efficiently compute the Grassmann coordinates of the code words.
The Grassmannian space $\Gr$ is the set of all $k-$dimensional subspaces of the vector space~\smash{$\F_q^n$}. Recently, codes in the Grassmannian have found an application in network coding. The main goal of this paper is to present…
Polar coding solutions demonstrate excellent performance under the list decoding that is challenging to implement in hardware due to the path sorting operations. As a potential solution to this problem, permutation decoding recently became…
Gray codes for vector spaces are considered in two graphs: the Grassmann graph, and the projective-space graph, both of which have recently found applications in network coding. For the Grassmann graph, constructions of cyclic optimal codes…
In this paper, we present an iterative construction of a polar code and develop properties of the dual of a polar code. Based on this approach, belief propagation of a polar code can be presented in the context of low-density parity check…
A lower bound on minimum distance of convolutional polar codes is provided. The bound is obtained from the minimum weight of generalized cosets of the codes generated by bottom rows of the polarizing matrix. Moreover, a construction of…
Arikan's polar codes are capable of achieving the Shannon's capacity at a low encoding and decoding complexity, while inherently supporting rate adaptation. By virtue of these attractive features, polar codes have provided fierce…