We consider the known list decoding algorithms for polar codes and compare their complexity.

A generalization of Arıkan’s polar code construction using transformations of the form G where G is an l × l matrix is considered. Necessary and sufficient conditions are given for these transformations to ensure channel polarization. It is shown that a large class of such transformations polarize symmetric binary-input memoryless channels.

We study polarization for nonbinary channels with input alphabet of size q = 2 , r = 2, 3, . . . . Using Arıkan’s polarizing kernel H2, we prove that the virtual channels that arise in the process of polarization converge to q-ary channels with capacity 1, 2, . . . , r bits, and that the total transmission rate approaches the symmetric capacity of the channel. This leads to an explicit transmis...

In contrast to the network security that relies on upper-layer encryption for confidentiality and authenticity of communications, physical layer (PLS) exploits uniqueness randomness channel encrypt information enhance system. this paper, we study PLS a polar-coded wireless communication To be more specific, leverage unique properties in polar code construction propose quality indicator (CQI)-ba...

Systematic polar codes are shown to outperform non-systematic polar codes in terms of the bit-error-rate (BER) performance. However theoretically the mechanism behind the better performance of systematic polar codes is not yet clear. In this paper, we set the theoretical framework to analyze the performance of systematic polar codes. The exact evaluation of the BER of systematic polar codes con...

In this paper, we propose the explicit construction of a new class of lattices based on polar codes, which are provably good for the additive white Gaussian noise (AWGN) channel. We follow the multilevel construction of Forney et al. (i.e., Construction D), where the code on each level is a capacityachieving polar code for that level. The proposed polar lattices are efficiently decodable by usi...

In this paper, we propose the explicit construction of a new class of lattices based on polar codes, which are provably good for the additive white Gaussian noise (AWGN) channel. We follow the multilevel construction of Forney et al. (i.e., Construction D), where the code on each level is a capacityachieving polar code for that level. The proposed polar lattices are efficiently decodable by usi...