Upper union bound for the decoding error probability of polar codes with arbitrary binary kernels under the successive cancelation decoding is derived. The proposed approach is based on the representation of polar codes as multilevel ones.

Study of polar codes in fading channels is of great importance when applying polar codes in wireless communications. Channel estimation is a fundamental step for communication to be possible in fading channels. For both systematic and non-systematic polar codes, construction of them is based on an information set and the known frozen bits. Efficient implementation of systematic and non-systemat...

A low-complexity systematic encoding algorithm for polar codes with Reed-Solomon kernel is presented. The proposed method relies on fast Fourier transform based ReedSolomon encoding techniques. Application of polar codes in storage systems is considered.

Polar codes are novel and efficient error correcting codes with low encoding and decoding complexities. These codes have a channel dependent generator matrix which is determined by the code dimension, code length and transmission channel parameters. This paper studies a variant of the McEliece public key cryptosystem based on polar codes, called"PKC-PC". Due to the fact that the structure of po...

Codes arising from Grassmannians have been widely investigated, both as generalization of Reed–Muller codes and for applications to network coding. Recently we introduced some new codes, arising from Polar Grassmannians, namely the set of all subspaces of a vector space F q which are totally singular with respect to a given non-degenerate quadratic form. The aim of the present paper is to prese...

We propose to reduce the decoding complexity of polar codes with non-Arikan kernels by employing a (near) ML decoding algorithm for the codes generated by kernel rows. A generalization of the order statistics algorithm is presented for soft decoding of Reed-Solomon codes. Algebraic properties of the Reed-Solomon code are exploited to increase the reprocessing order. The obtained algorithm is us...

The general subject considered in this thesis is a recently discovered coding technique, polar coding, which is used to construct a class of error correction codes with unique properties. In his ground-breaking work, Arıkan proved that this class of codes, called polar codes, achieve the symmetric capacity — the mutual information evaluated at the uniform input distribution — of any stationary ...

This paper proposes a polar code construction scheme that reduces constituent-code supplemented decoding latency. Constituent codes are the sub-codewords with specific patterns. They are used to accelerate the successive cancellation decoding process of polar code without any performance degradation. We modify the traditional construction approach to yield increased number of desirable constitu...

Polar codes are the first capacity achieving and efficiently implementable codes for classical communication. Recently they have also been generalized to communication over classical-quantum and quantum channels. In this work we present our recent results for polar coding in quantum information theory, including applications to classical-quantum multiple access channels, interference channels a...