Related papers: Polarization for arbitrary discrete memoryless cha…
We construct a channel coding scheme to achieve the capacity of any discrete memoryless channel based solely on the techniques of polar coding. In particular, we show how source polarization and randomness extraction via polarization can be…
Current deterministic algorithms for the construction of polar codes can only be argued to be practical for channels with small input alphabet sizes. In this paper, we show that any construction algorithm for channels with moderate input…
The polarization process of polar codes over a ternary alphabet is studied. Recently it has been shown that the scaling of the blocklength of polar codes with prime alphabet size scales polynomially with respect to the inverse of the gap…
We develop a low-complexity polar coding scheme for the discrete memoryless broadcast channel with confidential messages under strong secrecy and randomness constraints. Our scheme extends previous work by using an optimal rate of uniform…
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…
Ar{\i}kan's polar coding technique is based on the idea of synthesizing $n$ channels from the $n$ instances of the physical channel by a simple linear encoding transformation. Each synthesized channel corresponds to a particular input to…
Polar coding is a recently proposed coding technique that can provably achieve the channel capacity. The polar code structure, which is based on the original 2x2 generator matrix, polarises the channels, i.e., a portion of the channel…
The general subject considered in this thesis is a recently discovered coding technique, polar coding, which is used to construct a class of error correction codes with unique properties. In his ground-breaking work, Ar{\i}kan proved that…
It is shown that for any binary-input discrete memoryless channel $W$ with symmetric capacity $I(W)$ and any rate $R <I(W)$, the probability of block decoding error for polar coding under successive cancellation decoding satisfies $P_e \le…
The problem of polar coding for an arbitrary sequence of independent binary-input memoryless symmetric (BMS) channels $\left\{W_i\right\}_{i=1}^{N}$ is considered. The sequence of channels is assumed to be completely known to both the…
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…
We prove that, for all binary-input symmetric memoryless channels, polar codes enable reliable communication at rates within $\epsilon > 0$ of the Shannon capacity with a block length, construction complexity, and decoding complexity all…
A method to polarize channels universally is introduced. The method is based on combining two distinct channels in each polarization step, as opposed to Arikan's original method of combining identical channels. This creates an equal number…
Over any discrete memoryless channel, we build codes such that: for one, their block error probabilities and code rates scale like random codes'; and for two, their encoding and decoding complexities scale like polar codes'. Quantitatively,…
We prove polarization theorems for arbitrary classical-quantum (cq) channels. The input alphabet is endowed with an arbitrary Abelian group operation and an Ar{\i}kan-style transformation is applied using this operation. It is shown that as…
A generalization of the polar coding scheme called mixed-kernels is introduced. This generalization exploits several homogeneous kernels over alphabets of different sizes. An asymptotic analysis of the proposed scheme shows that its…
An algorithm is presented for approximating a single-user channel with a prime input alphabet size. The result is an upgraded version of the channel with a reduced output alphabet size. It is shown that this algorithm can be used to reduce…
This paper introduces techniques to construct binary polar source/channel codes based on the bit error probability of successive-cancellation decoding. The polarization lemma is reconstructed based on the bit error probability and then…
We show that the mismatched capacity of binary discrete memoryless channels can be improved by channel combining and splitting via Ar{\i}kan's polar transformations. We also show that the improvement is possible even if the transformed…
Achieving security against adversaries with unlimited computational power is of great interest in a communication scenario. Since polar codes are capacity achieving codes with low encoding-decoding complexity and they can approach perfect…