Related papers: Constructing Polar Codes Using Iterative Bit-Chann…
The min-sum approximation is widely used in the decoding of polar codes. Although it is a numerical approximation, hardly any penalties are incurred in practice. We give a theoretical justification for this. We consider the common case of a…
In this paper, we propose a construction for multi-kernel polar codes based on the maximization of the minimum distance. Compared to the original construction based on density evolution, our new design shows particular advantages for short…
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…
We introduce a new family of polar-like codes, called Partially Polarized Polar (PPP) codes. PPP codes are constructed from conventional polar codes by selectively pruning polarization kernels, thereby modifying the synthesized bit-channel…
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…
The construction of polar codes with code length $n=2^m$ involves $m$ layers of polar transforms. In this paper, we observe that after each layer of polar transforms, one can swap certain pairs of adjacent bits to accelerate the…
Polar codes are a class of linear error correction codes which provably attain channel capacity with infinite codeword lengths. Finite length polar codes have been adopted into the 5th Generation 3GPP standard for New Radio, though their…
An extension of polar codes is proposed, which allows some of the frozen symbols, called dynamic frozen symbols, to be data-dependent. A construction of polar codes with dynamic frozen symbols, being subcodes of extended BCH codes, is…
A polar coding scheme for fading channels is proposed in this paper. More specifically, the focus is Gaussian fading channel with a BPSK modulation technique, where the equivalent channel could be modeled as a binary symmetric channel with…
We exploit the redundancy of the language-based source to help polar decoding. By judging the validity of decoded words in the decoded sequence with the help of a dictionary, the polar list decoder constantly detects erroneous paths after…
When a neural network (NN) is used to decode a polar code, its training complexity scales exponentially as the code block size (or to be precise, as a number of message bits) increases. Therefore, existing solutions that use a neural…
A scheme for concatenating the recently invented polar codes with interleaved block codes is considered. By concatenating binary polar codes with interleaved Reed-Solomon codes, we prove that the proposed concatenation scheme captures the…
Polar codes have received growing attention in the past decade and have been selected as the coding scheme for the control channel in the fifth generation (5G) wireless communication systems. However, the conventional polar codes have only…
We prove two results on the universality of polar codes for source coding and channel communication. First, we show that for any polar code built for a source $P_{X,Z}$ there exists a slightly modified polar code - having the same rate, the…
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…
Systematic polar codes are shown to outperform non-systematic polar codes in terms of the bit-error-rate (BER) performance. However theoretically the mechanism behind the better performance of systematic polar codes is not yet clear. In…
Polar codes provably achieve the capacity of a wide array of channels under successive decoding. This assumes infinite precision arithmetic. Given the successive nature of the decoding algorithm, one might worry about the sensitivity of the…
Polar codes provably achieve the symmetric capacity of a memoryless channel while having an explicit construction. This work aims to increase the throughput of polar decoder hardware by an order of magnitude relative to the state of the art…
Channel coding over arbitrarily-permuted parallel channels was first studied by Willems et al. (2008). This paper introduces capacity-achieving polar coding schemes for arbitrarily-permuted parallel channels where the component channels are…
Polar codes are one of the most recent advancements in coding theory and they have attracted significant interest. While they are provably capacity achieving over various channels, they have seen limited practical applications.…