Related papers: An Efficient Construction Method Based on Partial …
Polar codes have received increasing attention in the past decade, and have been selected for the next generation of wireless communication standard. Most research on polar codes has focused on codes constructed from a $2\times2$…
Low degree Reed-Muller codes are known to satisfy local decoding properties which find applications in private information retrieval (PIR) protocols, for instance. However, their practical instantiation encounters a first barrier due to…
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.…
In this paper, we propose a comprehensive Polar coding solution that integrates reliability calculation, rate matching and parity-check coding. Judging a channel coding design from the industry's viewpoint, there are two primary concerns:…
In this paper, we investigate a novel family of polar codes based on multi-kernel constructions, proving that this construction actually polarizes. To this end, we derive a new and more general proof of polarization, which gives sufficient…
In this paper, we consider the application of Reed- Solomon (RS) channel coding for joint error correction and cooperative network coding on non-binary phase shift keying (PSK) modulated signals. The relay first decodes the RS channel coded…
Polarization-adjusted convolutional (PAC) codes combine the polar and convolutional transformations to enhance the distance properties of polar codes. They offer a performance very close to the finite length information-theoretic bounds for…
A framework of monomial codes is considered, which includes linear codes generated by the evaluation of certain monomials. Polar and Reed-Muller codes are the two best-known representatives of such codes and can be considered as two extreme…
Long Reed-Solomon (RS) codes are desirable for digital communication and storage systems due to their improved error performance, but the high computational complexity of their decoders is a key obstacle to their adoption in practice. As…
Polar codes form a very powerful family of codes with a low complexity decoding algorithm that attain many information theoretic limits in error correction and source coding. These codes are closely related to Reed-Muller codes because both…
Sphere decoding (SD) of polar codes is an efficient method to achieve the error performance of maximum likelihood (ML) decoding. But the complexity of the conventional sphere decoder is still high, where the candidates in a target sphere…
In this paper we present a novel modulation technique for dual polarization communication systems, which reduces the error rate compared with the existent schemes. This modulation places the symbols in a 3D constellation, rather than the…
In this paper, we leverage polar codes and the well-established channel polarization to design capacity-achieving codes with a certain constraint on the weights of all the columns in the generator matrix (GM) while having a low-complexity…
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…
The polar codes are proven to be capacity-achieving and are shown to have equivalent or even better finite-length performance than the turbo/LDPC codes under some improved decoding algorithms over the additive white Gaussian noise (AWGN)…
Most existing works of polar codes focus on the analysis of block error probability. However, in many scenarios, bit error probability is also important for evaluating the performance of channel codes. In this paper, we establish a new…
Reed-Muller (RM) codes exhibit good performance under maximum-likelihood (ML) decoding due to their highly-symmetric structure. In this paper, we explore the question of whether the code symmetry of RM codes can also be exploited to achieve…
A shortening method for large polarization kernels is presented, which results in shortened kernels with the highest error exponent if applied to kernels of size up to 32. It uses lower and upper bounds on partial distances for quick…
We consider explicit polar constructions of blocklength $n\rightarrow\infty$ for the two extreme cases of code rates $R\rightarrow1$ and $R\rightarrow0.$ For code rates $R\rightarrow1,$ we design codes with complexity order of $n\log n$ in…
This paper proposes a polar code construction scheme that reduces constituent-code supplemented decoding latency. Constituent codes are the sub-codewords with specific patterns. They are used to accelerate the successive cancellation…