Related papers: How to Construct Polar Codes
Polar codes were introduced in 2009 by Arikan as the first efficient encoding and decoding scheme that is capacity achieving for symmetric binary-input memoryless channels. Recently, this code family was extended by replacing the…
This paper investigates properties of polar codes that can be potentially useful in real-world applications. We start with analyzing the performance of finite-length polar codes over the binary erasure channel (BEC), while assuming belief…
Polar codes are a new family of error correction codes for which efficient hardware architectures have to be defined for the encoder and the decoder. Polar codes are decoded using the successive cancellation decoding algorithm that includes…
Improved bounds on the blocklength required to communicate over binary-input channels using polar codes, below some given error probability, are derived. For that purpose, an improved bound on the number of non-polarizing channels is…
This paper focuses on an improved Gaussian approximation (GA) based construction of polar codes with successive cancellation (SC) decoding over an additive white Gaussian noise (AWGN) channel. Arikan has proven that polar codes with…
In this paper, polar codes for the $m$-user multiple access channel (MAC) with binary inputs are constructed. It is shown that Ar{\i}kan's polarization technique applied individually to each user transforms independent uses of a $m$-user…
In this work, we present hardware and software implementations of flexible polar systematic encoders and decoders. The proposed implementations operate on polar codes of any length less than a maximum and of any rate. We describe the…
Polar codes are the first capacity achieving and efficiently implementable codes for classical communication. Recently they have also been generalized to communication over classical-quantum and quantum channels. In this work we present our…
Polar codes are designed for parallel binary-input additive white Gaussian noise (BiAWGN) channels with an average power constraint. The two main design choices are: the mapping between codeword bits and channels of different quality, and…
The polar transformation of a binary erasure channel (BEC) can be exactly approximated by other BECs. Ar{\i}kan proposed that polar codes for a BEC can be efficiently constructed by using its useful property. This study proposes a new class…
Recently, Ar{\i}kan introduced the method of channel polarization on which one can construct efficient capacity-achieving codes, called polar codes, for any binary discrete memoryless channel. In the thesis, we show that decoding algorithm…
The recently introduced polar codes constitute a breakthrough in coding theory due to their capacityachieving property. This goes hand in hand with a quasilinear construction, encoding, and successive cancellation list decoding procedures…
Polarization-adjusted convolutional (PAC) codes were recently proposed and arouse the interest of the channel coding community because they were shown to approach theoretical bounds for the (128,64) code size. In this letter, we propose…
Polar codes have attracted much recent attention as the first codes with low computational complexity that provably achieve optimal rate-regions for a large class of information-theoretic problems. One significant drawback, however, is that…
A practical rate-matching system for constructing rate-compatible polar codes is proposed. The proposed polar code circular buffer rate-matching is suitable for transmissions on communication channels that support hybrid automatic repeat…
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.…
In this paper, we investigate the fundamentals of puncturing and shortening for polar codes, based on binary domination which plays a key role in polar code construction. We first prove that the orders of encoder input bits to be made…
In this work, we introduce $\beta$-expansion, a notion borrowed from number theory, as a theoretical framework to study fast construction of polar codes based on a recursive structure of universal partial order (UPO) and polarization weight…
Among error-correcting codes, polar codes are the first to provably achieve channel capacity with an explicit construction. In this work, we present software implementations of a polar decoder that leverage the capabilities of modern…
A new algorithm for efficient exact maximum likelihood decoding of polar codes (which may be CRC augmented), transmitted over the binary erasure channel, is presented. The algorithm applies a matrix triangulation process on a sparse polar…