Related papers: Polar Codes: Characterization of Exponent, Bounds,…
We analyze polarization-adjusted convolutional codes using the algebraic representation of polar and Reed-Muller codes. We define a large class of codes, called generalized polynomial polar codes which include PAC codes and Reverse PAC…
We describe a successive-cancellation \emph{list} decoder for polar codes, which is a generalization of the classic successive-cancellation decoder of Ar{\i}kan. In the proposed list decoder, up to $L$ decoding paths are considered…
Suppose Alice wishes to send messages to Bob through a communication channel C_1, but her transmissions also reach an eavesdropper Eve through another channel C_2. The goal is to design a coding scheme that makes it possible for Alice to…
In this work, we investigate the performance of polar codes with the assistance of feedback in communication systems. Although it is well known that feedback does not improve the capacity of memoryless channels, we show that the finite…
It is shown that all polar encoding schemes of rate $R>\frac{1}{2}$ of block length $N$ implemented according to the Thompson VLSI model must take energy $E\ge\Omega\left(N^{3/2}\right)$. This lower bound is achievable up to polylogarithmic…
We survey coding techniques that enable reliable transmission at rates that approach the capacity of an arbitrary discrete memoryless channel. In particular, we take the point of view of modern coding theory and discuss how recent advances…
Polar codes are a new class of error correcting linear block codes, whose generator matrix is specified by the knowledge of transmission channel parameters, code length and code dimension. Moreover, regarding computational security, it is…
Polar codes are a channel coding scheme for the next generation of wireless communications standard (5G). The belief propagation (BP) decoder allows for parallel decoding of polar codes, making it suitable for high throughput applications.…
Motivated by the need for channel codes with low-complexity soft-decision decoding algorithms, we consider the recursive Plotkin concatenation of optimal low-rate and high-rate codes based on simplex codes and their duals. These component…
Recently, automorphism ensemble decoding (AED) has drawn research interest as a more computationally efficient alternative to successive cancellation list (SCL) decoding of polar codes. Although AED has demonstrated superior performance for…
Polar codes are capacity-achieving error-correcting codes with an explicit construction that can be decoded with low-complexity algorithms. In this work, we show how the state-of-the-art low-complexity decoding algorithm can be improved to…
This paper presents the first proof of polarization for the deletion channel with a constant deletion rate and a regular hidden-Markov input distribution. A key part of this work involves representing the deletion channel using a trellis…
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…
In this paper, the analysis of the performance of the concatenation of a short polar code with an outer binary linear block code is addressed from a distance spectrum viewpoint. The analysis targets the case where an outer cyclic code is…
Tailoring polar code construction for decoding algorithms beyond successive cancellation has remained a topic of significant interest in the field. However, despite the inherent nested structure of polar codes, the use of sequence models in…
We consider the problem of supporting H-ARQ with polar codes. For supporting H-ARQ, we propose to create redundancy versions based on different, but equivalent, subsets of a polar code. The equivalent subsets are created from an initial…
The polarization decomposition of arbitrary binary-input memoryless channels (BMCs) is studied in this work. By introducing the polarization factor (PF), defined in terms of the conditional entropy of the channel output under various input…
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…
In this paper, we show some applications of algebraic curves to the construction of kernels of polar codes over a discrete memoryless channel which is symmetric w.r.t the field operations. We will also study the minimum distance of the…
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…