Related papers: Construction of polar codes for arbitrary discrete…
In the low-energy high-energy-efficiency regime of classical optical communications---relevant to deep-space optical channels---there is a big gap between reliable communication rates achievable via conventional optical receivers and the…
Polar codes, introduced recently by Ar\i kan, are the first family of codes known to achieve capacity of symmetric channels using a low complexity successive cancellation decoder. Although these codes, combined with successive cancellation,…
Polar codes are constructed based on the reliability of sub-channels resulting from the polarization effect. However, this information-theoretic construction approach leads to a poor weight distribution. To address this issue,…
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…
We consider classical-quantum (cq-)channels with memory, and establish that Ar{\i}kan-constructed polar codes achieve the classical capacity for two key noise models, namely for (i) qubit erasures and (ii) unital qubit noise with channel…
For the polar codes introduced by Arikan in 2009, the first code family achieving the capacity of binary-input discrete memoryless channels (BIDMCs) with low-complexity encoding and decoding, it is crucial to evaluate the reliability of the…
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…
It is well known that to fulfill their full potential, the design of polar codes must be tailored to their intended decoding algorithm. While for successive cancellation (SC) decoding, information theoretically optimal constructions are…
Polar code visibly approaches channel capacity in practice and is thereby a constituent code of the 5G standard. Compared to low-density parity-check code, however, the performance of short-length polar code has rooms for improvement that…
In this work, we present a family of architectures for polar decoders using a reduced-complexity successive-cancellation decoding algorithm that employs unrolling to achieve extremely high throughput values while retaining moderate…
We construct a joint coordination-channel polar coding scheme for strong coordination of actions between two agents $\mathsf X$ and $\mathsf Y$, which communicate over a discrete memoryless channel (DMC) such that the joint distribution of…
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 provide a generalization of quantum polar codes to quantum channels with qudit-input, achieving the symmetric coherent information of the channel. Our scheme relies on a channel combining and splitting construction, where a two-qudit…
The recently-discovered polar codes are seen as a major breakthrough in coding theory; they provably achieve the theoretical capacity of discrete memoryless channels using the low complexity successive cancellation (SC) decoding algorithm.…
Polar codes are a family of capacity-achieving error-correcting codes, and they have been selected as part of the next generation wireless communication standard. Each polar code bit-channel is assigned a reliability value, used to…
It is shown that polar coding schemes achieve the known achievable rate regions for several multi-terminal communications problems including lossy distributed source coding, multiple access channels and multiple descriptions coding. The…
Multi-kernel polar codes have recently been proposed to construct polar codes of lengths different from powers of two. Decoder implementations for multi-kernel polar codes need to account for this feature, that becomes critical in memory…
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…
Reed Muller (RM) codes are known for their good minimum distance. One can use their structure to construct polar-like codes with good distance properties by choosing the information set as the rows of the polarization matrix with the…
Herein, we focus on explicit constructions of $\ell\times\ell$ binary kernels with small scaling exponent for $\ell \le 64$. In particular, we exhibit a sequence of binary linear codes that approaches capacity on the BEC with quasi-linear…