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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…
Polarization-adjusted convolutional (PAC) codes, as a concatenated coding scheme based on polar codes, is able to approach the finite-length bound of binary-input AWGN channel at short blocklengths. In this paper, we extend PAC codes to the…
An efficient implementation of min-sum SC/list decoding of convolutional polar codes is proposed. The complexity of the proposed implementation of SC decoding is more than two times smaller than the straightforward implementation. Moreover,…
Due to the advantage of capacity-achieving, polar codes have been extended to the block fading channel whereas most constructions involve complex iterative-calculation. In this paper, we establish a systematic framework to analyze the error…
Deep polar codes are pre-transformed polar codes that employ a multi-layered polar kernel transformation strategy to enhance code performance in short blocklength regimes. However, like conventional polar codes, their block length is…
Polar code, with explicit construction and recursive structure, is the latest breakthrough in channel coding field for its low-complexity and theoretically capacity-achieving property. Since polar codes can approach the maximum likelihood…
Polar codes are a class of {\bf structured} channel codes proposed by Ar{\i}kan based on the principle of {\bf channel polarization}, and can {\bf achieve} the symmetric capacity of any Binary-input Discrete Memoryless Channel (B-DMC). The…
The growth rate of the weight distribution of irregular doubly-generalized LDPC (D-GLDPC) codes is developed and in the process, a new efficient numerical technique for its evaluation is presented. The solution involves simultaneous…
In this article, we provide a complete characterization of codewords in polar codes with weights less than twice the minimum distance, using the group action of the lower triangular affine (LTA) group. We derive a closed-form formula for…
We study the high-dimensional linear regression problem with categorical predictors that have many levels. We propose a new estimation approach, which performs model compression via two mechanisms by simultaneously encouraging (a)…
Cyclic codes are an important class of linear codes, whose weight distribution have been extensively studied. So far, most of previous results obtained were for cyclic codes with no more than three zeros. Recently, \cite{Y-X-D12}…
The duals of cyclic codes with two zeros have been extensively studied, and their weight distributions have recently been evaluated in some cases. In this note, we determine the weight distribution of a certain new class of such codes by…
Given a binary nonlinear code, we provide a deterministic algorithm to compute its weight and distance distribution, and in particular its minimum weight and its minimum distance, which takes advantage of fast Fourier techniques. This…
Weighted voting is a conventional approach to improving the performance of replicated systems based on commonly-used majority quorum systems in heterogeneous environments. In long-lived systems, a weight reassignment protocol is required to…
Long polar codes can achieve the symmetric capacity of arbitrary binary-input discrete memoryless channels under a low complexity successive cancelation (SC) decoding algorithm. However, for polar codes with short and moderate code length,…
The successive cancellation list decoding algorithm for polar codes yields near-optimal decoding performance at the cost of high implementation complexity. The successive cancellation stack algorithm has been shown to provide similar…
Given complex numbers $w_1, \ldots, w_n$, we define the weight $w(X)$ of a set $X$ of 0-1 vectors as the sum of $w_1^{x_1} \cdots w_n^{x_n}$ over all vectors $(x_1, \ldots, x_n)$ in $X$. We present an algorithm, which for a set $X$ defined…
Determining the weight distribution of a linear code is a classical and fundamental topic in coding theory that has been extensively investigated. Repeated-root cyclic codes, which form a significant subclass of error-correcting codes, have…
Product codes are widespread in optical communications, thanks to their high throughput and good error-correction performance. Systematic polar codes have been recently considered as component codes for product codes. In this paper, we…
In this expository paper we show how one can, in a uniform way, calculate the weight distributions of some well-known binary cyclic codes. The codes are related to certain families of curves, and the weight distributions are related to the…