Related papers: A Class of Transformations that Polarize Symmetric…
Polar codes, introduced by Arikan, achieve symmetric capacity of any discrete memoryless channels under low encoding and decoding complexity. Recently, non-binary polar codes have been investigated. In this paper, we calculate error…
Let $W$ be a channel where the input alphabet is endowed with an Abelian group operation, and let $(W_n)_{n\geq 0}$ be Ar{\i}kan's channel-valued polarization process that is obtained from $W$ using this operation. We prove that the process…
Polar codes, invented by Arikan in 2009, are known to achieve the capacity of any binary-input memoryless output-symmetric channel. One of the few drawbacks of the original polar code construction is that it is not universal. This means…
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…
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…
Polarization phenomenon over any finite field $\mathbb{F}_{q}$ with size $q$ being a power of a prime is considered. This problem is a generalization of the original proposal of channel polarization by Arikan for the binary field, as well…
Being attracted by the property of classical polar code, researchers are trying to find its analogue in quantum fields, which is called quantum polar code. The first step and the key to design quantum polar code is to find out for the…
Polar codes are constructed for m-user multiple access channels (MAC) whose input alphabet size is a prime number. The block error probability under successive cancelation decoding decays exponentially with the square root of the block…
In this paper we investigate, starting with a symmetric B-DMC, the evolution of various probabilities of the likelihood ratios of the synthetic channels created by the recursive application of the basic polarization transformations. The…
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…
A framework is proposed that allows for a joint description and optimization of both binary polar coding and $2^m$-ary digital pulse-amplitude modulation (PAM) schemes such as multilevel coding (MLC) and bit-interleaved coded modulation…
Polar codes are introduced for discrete memoryless broadcast channels. For $m$-user deterministic broadcast channels, polarization is applied to map uniformly random message bits from $m$ independent messages to one codeword while…
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…
Reed-Muller (RM) codes and polar codes are generated by the same matrix $G_m= \bigl[\begin{smallmatrix}1 & 0 \\ 1 & 1 \\ \end{smallmatrix}\bigr]^{\otimes m}$ but using different subset of rows. RM codes select simply rows having largest…
Arikan's polar coding method is extended to two-user multiple-access channels. It is shown that if the two users of the channel use the Arikan construction, the resulting channels will polarize to one of five possible extremals, on each of…
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…
We consider the problem of efficiently constructing polar codes over binary memoryless symmetric (BMS) channels. The complexity of designing polar codes via an exact evaluation of the polarized channels to find which ones are "good" appears…
We introduce the design of a set of code sequences $ \{ {\mathscr C}_{n}^{(m)} : n\geq 1, m \geq 1 \}$, with memory order $m$ and code-length $N=O(\phi^n)$, where $ \phi \in (1,2]$ is the largest real root of the polynomial equation…
The construction of polar codes for channels other than BECs requires sorting of all bit channels and then selecting the best $K$ of them for a block length $N=2^n$. In this paper, two types of partial orders (PO) of polar codes are…
Polar codes were introduced by Arikan in 2008 and are the first family of error-correcting codes achieving the symmetric capacity of an arbitrary binary-input discrete memoryless channel under low complexity encoding and using an efficient…