Related papers: Reed-Muller codes polarize
A multilevel coded modulation scheme is studied that uses solely binary polar codes and Honda-Yamamoto probabilistic shaping. The scheme is shown to achieve the capacity of discrete memoryless channels with input alphabets of cardinality a…
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 present a novel iterative decoding algorithm for Reed-Muller (RM) codes, which takes advantage of a graph representation of the code. Vertices of the considered graph correspond to codewords, with two vertices being connected by an edge…
Polarization-adjusted convolutional (PAC) codes are a new family of linear block codes that can perform close to the theoretical bounds in the short block-length regime. These codes combine polar coding and convolutional coding. In this…
Over the past years, Polar codes have arisen as a highly effective class of linear codes, equipped with a decoding algorithm of low computational complexity. This family of codes share a common algebraic formalism with the well-known…
We present an approach to showing that a linear code is resilient to random errors. We use this approach to obtain decoding results for both transitive codes and Reed-Muller codes. We give three kinds of results about linear codes in…
Bit-interleaved coded modulation (BICM) and multilevel coded modulation (MLC) are commonly used to combine polar codes with high order modulation. While BICM benefits from simple design and the separation of coding and modulation, MLC shows…
New soft- and hard decision decoding algorithms are presented for general Reed-Muller codes $\left\{\genfrac{}{}{0pt}{}{m}{r}\right\} $ of length $2^{m}$ and distance $2^{m-r}$. We use Plotkin $(u,u+v)$ construction and decompose code…
Arikan's recursive code construction is designed to polarize a collection of memoryless channels into a set of good and a set of bad channels, and it can be efficiently decoded using successive cancellation. It was recently shown that the…
$2^m$-ary modulation creates $m$ bit channels which are neither independent nor identical, and this causes problems when applying polar coding because polar codes are designed for independent identical channels. Different from the existing…
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,…
Reed-Muller codes are studied for peak power control in multicarrier code-division multiple access (MC-CDMA) communication systems. In a coded MC-CDMA system, the information data multiplexed from users is encoded by a Reed-Muller subcode…
Recently, a purely quantum version of polar codes has been proposed in [1] based on a quantum channel combining and splitting procedure, where a randomly chosen two-qubit Clifford unitary acts as channel combining operation. Here, we…
Polar coding over a class of binary discrete memoryless channels with channel knowledge at the encoder is studied. It is shown that polar codes achieve the capacity of convex and one-sided classes of symmetric channels.
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…
Constructing a polar code is all about selecting a subset of rows from a Kronecker power of $[^1_1{}^0_1]$. It is known that, under successive cancellation decoder, some rows are Pareto-better than the other. For instance, whenever a user…
Multilevel coding (MLC) is a coded modulation technique which can achieve excellent performance over a range of communication channels. Polar codes have been shown to be quite compatible with communication systems using MLC, as the rate…
This paper formulates the polar-code construction problem for the successive-cancellation list (SCL) decoder as a maze-traversing game, which can be solved by reinforcement learning techniques. The proposed method provides a novel technique…
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…
Code decompositions (a.k.a code nestings) are used to design good binary polar code kernels. The proposed kernels are in general non-linear and show a better rate of polarization under successive cancelation decoding, than the ones…