Related papers: Partial Orders in Rate-Matched Polar Codes
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…
Consider the problem of constructing a polar code of block length $N$ for the transmission over a given channel $W$. Typically this requires to compute the reliability of all the $N$ synthetic channels and then to include those that are…
In many practical communication systems, one binary encoder/decoder pair is used to communicate over a set of parallel channels. Examples of this setup include multi-carrier transmission, rate-compatible puncturing of turbo-like codes, and…
In this work, a novel data-driven methodology for designing polar codes for channels with and without memory is proposed. The methodology is suitable for the case where the channel is given as a "black-box" and the designer has access to…
-We develop a polar coding scheme for empirical coordination in a two-node network with a noisy link in which the input and output signals have to be coordinated with the source and the reconstruction. In the case of non-causal encoding and…
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…
For a binary-input memoryless symmetric channel $W$, we consider the asymptotic behavior of the polarization process in the large block-length regime when transmission takes place over $W$. In particular, we study the asymptotics of the…
In this paper, we present an extension of the semidefinite programming formulation of the optimal rate code design in single link Binary Erasure Channel (BEC) proposed by the authors to the Binary Erasure Multiple Access Channel (BE-MAC)…
In this paper, we derive analytic expressions for the success probability of decoding (Partial) Unit Memory codes in memoryless channels. An applications of this result is that these codes outperform individual block codes in certain…
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…
Polar codes have become one of the most favorable capacity achieving error correction codes (ECC) along with their simple encoding method. However, among the very few prior successive cancellation (SC) polar decoder designs, the required…
Polar codes are the latest breakthrough in coding theory, as they are the first family of codes with explicit construction that provably achieve the symmetric capacity of discrete memoryless channels. Ar{\i}kan's polar encoder and…
Polar codes are designed for parallel binary-input additive white Gaussian noise (BiAWGN) channels with an average power constraint. The two main design choices are: the mapping between codeword bits and channels of different quality, and…
We develop component evolution (CE), a framework based on complex function theory for finite-blocklength channel polarization on discrete binary-input memoryless output-symmetric (BMS) channels. In this view, the Bhattacharyya parameter is…
A method for efficiently constructing polar codes is presented and analyzed. Although polar codes are explicitly defined, straightforward construction is intractable since the resulting polar bit-channels have an output alphabet that grows…
The recently-discovered polar codes are widely seen as a major breakthrough in coding theory. These codes achieve the capacity of many important channels under successive cancellation decoding. Motivated by the rapid progress in the theory…
We consider polar codes constructed from the $2\times 2$ kernel $\begin{bmatrix} 1 & 0 \\ \alpha & 1 \end{bmatrix}$ over a finite field $\mathbb{F}_{q}$, where $q=p^s$ is a power of a prime number $p$, and $\alpha$ satisfies that…
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…
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…
In this paper, we design explicit codes for strong coordination in two-node networks. Specifically, we consider a two-node network in which the action imposed by nature is binary and uniform, and the action to coordinate is obtained via a…