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...

A new family of codes based on polar codes, soft concatenation and list+CRC decoding is proposed. Numerical experiments show the performance competitive with industry standards and Tal, Vardy approach.

We introduce the design of a set of code sequences tC n : n ě 1,m ě 1u, with memory order m and code-length N “ Opφq, where φ P p1, 2s is the largest real root of the polynomial equation F pm, ρq “ ρm ́ρm ́1 ́1 and φ is decreasing in m. tC n u is based on the channel polarization idea, where tC n u coincides with the polar codes presented by Arıkan in [1] and can be encoded and decoded with comple...

An extension of the stack decoding algorithm for polar codes is presented. The paper introduces a new score function, which enables one to accurately compare paths of different length. This results in significant complexity reduction with respect to the original stack algorithm at the expense of negligible performance loss.

An algorithm is presented for approximating a single-user channel with a prime input alphabet size. The result is an upgraded version of the channel with a reduced output alphabet size. It is shown that this algorithm can be used to reduce the output alphabet size to the input alphabet size in most cases.

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

Abstract In actual communication scenarios, wireless transmission channels have the nature of heterogeneity. order to ensure that data can be transmitted with high reliability and low delay, this paper designs a quasi-optimal polar code adapt various channel environments, which called Q-polar code. Based on polarization theory codes state information (CSI), index set is designed constructed per...

˗ Polar codes are provably capacity achieving linear block codes. The generator matrix of these codes is specified by knowing the parameters of transmission channel, length and dimension of the used code. On the other hand, for the cryptosystems based on general decoding problem (i.e. code based cryptosystems), the generator matrix of the applied code should be properly hidden from the attacker...

We consider the problem of polar coding for the 2-user discrete memoryless interference channel (DM-IC). Existing schemes are designed according to the original description of the Han-Kobayashi region, which involves two deterministic functions that map auxiliary random variables to channel inputs. Inspired by Chong et al.’s compact description of the Han-Kobayashi region, we propose a novel, s...

We consider the joint design of polar coding and higher-order modulation schemes for ever increased spectral efficiency. The close connection between the polar code construction and the multi-level coding approach is described in detail. Relations between different modulation schemes such as bit-interleaved coded modulation (BICM) and multi-level coding (MLC) in case of polar-coded modulation a...