Polar Code Design for Irregular Multidimensional Constellations

Irregular sampling for multidimensional polar processing of integral transforms

We survey a family of theories that enable to process polar data via integral transforms. We show the relation between irregular sampling and discrete integral transforms, demonstrate the application of irregular (polar) sampling to image processing problems, and derive approximation algorithms that are based on unequally spaced samples. It is based on sampling the Fourier domain. We describe 2...

Strange Attractor for Efficient Polar Code Design

This paper presents a definition of a construction for long polar codes. Recently, we know that partial order is a universal property of the construction with a sublinear complexity for polar codes. In order to describe the partial order, addition and left-swap operators are only defined as universal up to now. In this study, we first propose 1 + log2 log2 N universal operators to describe mult...

Irregular Signal Constellations , Mappings and Precoder

This paper investigates adaptive bit-interleaved coded modulation (BICM) with different iterative decoding schemes for bandwidth efficient transmission. We assume knowledge of the average channel quality at the transmitter. For a fixed modulation scheme, the bandwidth efficiency can be adapted to the channel quality by changing the channel code rate and the iterative decoding procedure can be o...

Irregular Sampling for Multidimensional Polar Processing of Integral Transforms and Prolate Spheroidal Wave Functions

Analyzing physical phenomena using a computer inevitably requires to bridge between the continuous nature of the physical phenomena and the discrete nature of computers. This bridging is known as sampling. The continuous signal is sampled such that it is represented by a discrete set of samples. The sampling scheme used to discretize the signal is often irregular. This may be due to either the ...

Polar code design and decoding for magnetic recording