Related papers: Re-proving Channel Polarization Theorems: An Extre…
We introduce a new class of circuits for constructing efficiently decodable error-correction codes, based on a recently discovered contractible tensor network. We perform an in-depth study of a particular example that can be thought of as…
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…
Polar codes are the first proven capacity-achieving codes. Recently, they are adopted as the channel coding scheme for 5G due to their superior performance.A polar code for encoding length-K information bits in length-N codeword could be…
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…
The recently-discovered polar codes are seen as a major breakthrough in coding theory; they provably achieve the theoretical capacity of discrete memoryless channels using the low complexity successive cancellation (SC) decoding algorithm.…
We show that the entire class of polar codes (up to a natural necessary condition) converge to capacity at block lengths polynomial in the gap to capacity, while simultaneously achieving failure probabilities that are exponentially small in…
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…
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…
Polar codes have emerged as the most favorable channel codes for their unique capacity-achieving property. To date, numerous works have been reported for efficient design of polar codes decoder. However, these prior efforts focused on…
In this paper, we study the symmetry of polar codes on symmetric binary-input discrete memoryless channels (B-DMC). The symmetry property of polar codes is originally pointed out in Arikan's work for general B-DMC channels. With the…
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…
Improved bounds on the blocklength required to communicate over binary-input channels using polar codes, below some given error probability, are derived. For that purpose, an improved bound on the number of non-polarizing channels is…
We introduce a new family of polar-like codes, called Partially Polarized Polar (PPP) codes. PPP codes are constructed from conventional polar codes by selectively pruning polarization kernels, thereby modifying the synthesized bit-channel…
An implementation-efficient finite alphabet decoder for polar codes relying on coarsely quantized messages and low-complexity operations is proposed. Typically, finite alphabet decoding performs concatenated compression operations on the…
We introduce explicit schemes based on the polarization phenomenon for the tasks of one-way secret key agreement from common randomness and private channel coding. For the former task, we show how to use common randomness and insecure…
In this work, we address the low-complexity construction of shortened and punctured polar codes from a unified view. While several independent puncturing and shortening designs were attempted in the literature, our goal is a unique,…
We study the application of polar codes in deletion channels by analyzing the cascade of a binary erasure channel (BEC) and a deletion channel. We show how polar codes can be used effectively on a BEC with a single deletion, and propose a…
Polar coding gives rise to the first explicit family of codes that provably achieve capacity with efficient encoding and decoding for a wide range of channels. However, its performance at short block lengths is far from optimal. Arikan has…
We analyze the trade-off between the undetected error probability (i.e., the probability that the channel decoder outputs an erroneous message without detecting the error) and the total error probability in the short blocklength regime. We…
Similar to existing codes, puncturing and shortening are two general ways to obtain an arbitrary code length and code rate for polar codes. When some of the coded bits are punctured or shortened, it is equivalent to a situation in which the…