Fast polarization is crucial for the performance guarantees of polar codes. In the memoryless setting, the rate of polarization is known to be exponential in the square root of the block length. A complete characterization of the rate of polarization for models with memory has been missing. We consider polar codes for processes with memory that are characterized by an underlying ergodic finite ...

Gopalan, Klivans, and Zuckerman proposed a list-decoding algorithm for Reed-Muller codes. Their algorithm works up to a given list-decoding radius. Dumer, Kabatiansky, and Tavernier improved the complexity of the algorithm for binary Reed-Muller codes by using wellknown Plotkin construction. In this study, we propose a list-decoding algorithm for non-binary Reed-Muller codes as a natural genera...

We prove that, for the binary erasure channel (BEC), polar-coding paradigm gives rise to codes that not only approach Shannon limit but do so under best possible scaling of their block length as a function gap capacity. This result exhibits first known family attain both optimal and quasi-linear complexity encoding decoding. Our proof is based on construction analysis polar with large kernels. ...

In this report, we review the construction of polar codes and we briefly present the main results that lead to the conclusion that polar codes are capacity achieving over binaryinput discrete memoryless channels. Moreover, we discuss a more sophisticated variant of successive cancellation decoding, namely list successive cancellation decoding, that aims to improve the finite-length performance ...

A NON-ASYMPTOTIC APPROACH TO THE ANALYSIS OF COMMUNICATION NETWORKS: FROM ERROR CORRECTING CODES TO NETWORK PROPERTIES MAY 2013 ALI ESLAMI B.Sc., SHARIF UNIVERSITY OF TECHNOLOGY M.Sc., SHARIF UNIVERSITY OF TECHNOLOGY Ph.D., UNIVERSITY OF MASSACHUSETTS AMHERST Directed by: Professor Hossein Pishro-Nik This dissertation has its focus on two different topics: 1. non-asymptotic analysis of polar co...

We consider the problem of supporting H-ARQ with polar codes. For supporting H-ARQ, we propose to create redundancy versions based on different, but equivalent, subsets of a polar code. The equivalent subsets are created from an initial subset of a polar code using an inherent symmetry in polar code construction. A greedy construction is used to create the initial subset of a polar code. We dem...

Polar codes are the first family of error correcting codes that provably achieve the capacity of symmetric binary-input discrete memoryless channels with low complexity. Since the development of polar codes, there have been many studies to improve their finite-length performance. As a result, polar codes are now adopted as a channel code for the control channel of 5G new radio of the 3rd genera...

Shannon’s monumental 1948 work laid the foundations for the rich fields of information and coding theory. The quest for efficient coding schemes to approach Shannon capacity has occupied researchers ever since, with spectacular progress enabling the widespread use of error-correcting codes in practice. Yet the theoretical problem of approaching capacity arbitrarily closely with polynomial compl...

This work is on fast encoding and decoding of polar codes. We propose and detail 8-bit and 16-bit parallel decoders that can be used to reduce the decoding latency of the successive-cancellation decoder. These decoders are universal and can decode flexible-rate and flexible-length polar codes. We also present fast encoders that can be used to increase the throughput of serially-implemented pola...