Polar codes, that have been recently introduced by Arikan, are one of the first codes that achieved the capacity for vast numerous channels and they also have low complexity in symmetric memoryless channels. Polar codes are constructed based on a phenomenon called channel polarization. This paper discusses relay channel polarization in order to achieve the capacity and show that if inputs of tw...

In this paper, we propose a new framework for joint encryption encoding scheme based on polar codes, namely efficient and secure joint secret key encryption channel coding scheme. The issue of using new coding structure, i.e. polar codes in Rao-Nam (RN) like schemes is addressed. Cryptanalysis methods show that the proposed scheme has an acceptable level of security with a relatively smaller ke...

Over any discrete memoryless channel, we build codes such that: for one, their block error probabilities and code rates scale like random codes'; two, encoding decoding complexities polar codes'. Quantitatively, constants $\pi,\rho>0$ that $\pi+2\rho<1$, construct a sequence of correction with length $N$ approaching infinity, probability $\exp(-N^\pi)$, rate $N^{-\rho}$ less than the Shannon ca...

Introduction: Polar codes are a major breakthrough in coding theory [1]. They can achieve Shannon capacity with a simple encoder and a simple successive cancellation (SC) decoder, both with low complexity of the order of ( ) N N log O , where N is the code block size. But for short and moderate lengths, the error rate performance of polar codes with the SC decoding is not as good as LDPC or tur...

In this paper, we propose a new class of nonbinary polar codes with two-stage polarization, where the outer polarization (symbol-level polarization) kernel is a nonbinary matrix resembling Arıkan’s kernel, and the inner polarization (bit-level polarization) kernel is a properly designed binary matrix. The encoder/decoder of the proposed nonbinary polar codes have the same structure as the origi...

Polar codes under successive cancellation decoding proposed by Ar{\i}kan provably achieve the symmetric capacity of any given binary-input discrete memoryless channel. The successive cancellation list decoder for polar codes was described by Tal and Vardy as a generalization of the successive cancellation decoder of Ar{\i}kan. The performance of the successive cancellation list decoder is encou...