We present a comparative study of the performance of various polar code constructions in an additive white Gaussian noise (AWGN) channel. A polar code construction is any algorithm that selects K best among N possible polar bit-channels at the design signal-to-noise-ratio (design-SNR) in terms of bit error rate (BER). Optimal polar code construction is hard and therefore many suboptimal polar c...

A new cooperative punctured polar coding (CPPC) scheme with multi joint successive cancellation (MJSC) decoding at the destination is proposed, which may be obtained by applying puncturing algorithm to cooperative polar coding scenario. In this proposed algorithm we generate a cooperative scheme for punctured polar codes with various code lengths by employing the reduction of the general polari...

We consider two problems related to polar codes. First is the problem of polar codes construction and analysis of their performance without Monte-Carlo method. The formulas proposed are the same as those in [Mori-Tanaka], yet we believe that our approach is original and has clear advantages. The resulting computational procedure is presented in a fast algorithm form which can be easily implemen...

A heuristic construction of polar codes for successive cancellation list (SCL) decoding with a given list size is proposed to balance the trade-off between performance measured in frame error rate (FER) and decoding complexity. Furthermore, a construction based on dynamically frozen bits with constraints among the ”low weight bits” (LWB) is presented. Simulation results show that the LWB-polar ...

Hyperplane codes are a class of convex codes that arise as the output of a one layer feed-forward neural network. Here we establish several natural properties of nondegenerate hyperplane codes, in terms of the polar complex of the code, a simplicial complex associated to any combinatorial code. We prove that the polar complex of a non-degenerate hyperplane code is shellable and show that all cu...

Polar codes are the first explicit code sequences that provably achieve capacity for discrete memory-less channels. However, their performance with successive cancellation (SC) decoding is unimpressive at practical block-lengths. In this paper, we propose a scheme of concatenating Reed-Solomon (RS) with modified polar codes to improve the performance of SC. Firstly, short repetition block codes...

The structure of polar codes inherently requires block lengths to be powers of two. In this paper, we investigate how different block lengths can be realized by coupling of several short-length polar codes. For this, we first analyze “code augmentation” to better protect the semipolarized channels, improving the BER performance under belief propagation decoding. Several serial and parallel augm...

In this note we offer a short summary of the content of the lecture on polar Grassmann codes given at the Indian Intitute of Technology, Mumbai, during the International Conference on Algebraic Geometry and Coding Theory in December 2013. More precisely, we consider the codes arising from the projective system determined by the image ε k (∆k) of the Grassmann embedding ε gr k of an orthogonal G...

This tutorial treats the fundamentals of polarization theory and polar coding. Arıkan’s original results on binary source and channel polarization methods are studied. Error probability and complexity analyses are offered. The original results are generalized in several directions. Early developments in the field are discussed, pointers to some of the important work omitted from this tutorial a...