相关论文: Explicit Polar Codes with Small Scaling Exponent

A binary code Enc$:\{0,1\}^k \to \{0,1\}^n$ is $(0.5-\epsilon,L)$-list decodable if for all $w \in \{0,1\}^n$, the set List$(w)$ of all messages $m \in \{0,1\}^k$ such that the relative Hamming distance between Enc$(m)$ and $w$ is at most…

We consider the Calder\'on-Zygmund kernels $K_ {\alpha,n}(x)=(x_i^{2n-1}/|x|^{2n-1+\alpha})_{i=1}^d$ in $\mathbb{R}^n$ for $0<\alpha\leq 1$ and $n\in\mathbb{N}$. We show that, on the plane, for $0<\alpha<1$, the capacity associated to the…

Polar codes provably achieve the capacity of a wide array of channels under successive decoding. This assumes infinite precision arithmetic. Given the successive nature of the decoding algorithm, one might worry about the sensitivity of the…

The generator matrices of polar codes and Reed-Muller codes are obtained by selecting rows from the Kronecker product of a lower-triangular binary square matrix. For polar codes, the selection is based on the Bhattacharyya parameter of the…

This paper describes the 2018 Planck CMB likelihoods, following a hybrid approach similar to the 2015 one, with different approximations at low and high multipoles, and implementing several methodological and analysis refinements. With more…

We prove polarization theorems for arbitrary classical-quantum (cq) channels. The input alphabet is endowed with an arbitrary Abelian group operation and an Ar{\i}kan-style transformation is applied using this operation. It is shown that as…

We study the single and double lepton polarization asymmetries in the semileptonic $B$ meson decays $B \to K_1 (1270) \ell^+ \ell^-$ $\ell \equiv e$, $\mu$, $\tau$), where the strange $P$-wave meson, $K_1(1270)$, is the mixtures of the…

Polar codes are constructed for m-user multiple access channels (MAC) whose input alphabet size is a prime number. The block error probability under successive cancelation decoding decays exponentially with the square root of the block…

A general framework is proposed that includes polar codes over arbitrary channels with arbitrary kernels. The asymptotic tradeoff among block length $N$, code rate $R$, and error probability $P$ is analyzed. Given a tradeoff between $N,P$…

Each memoryless binary-input channel (BIC) can be uniquely described by its Blackwell measure, which is a probability distribution on the unit interval $[0,1]$ with mean $1/2$. Conversely, any such probability distribution defines a BIC.…

Sorting operation is one of the main bottlenecks for the successive-cancellation list (SCL) decoding. This paper introduces an improvement to the SCL decoding for polar and pre-transformed polar codes that reduces the number of sorting…

Using grand canonical Monte Carlo simulations, we investigate the percolation behavior of a square well fluid with an ultra-short range of attraction in three dimension (3D) and in confined geometry. The latter is defined through two…

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 representations of positive definite kernels $K$ in a general setting, but with view to applications to harmonic analysis, to metric geometry, and to realizations of certain stochastic processes. Our initial results are stated for…

The paper studies scaling limits of random skew plane partitions confined to a box when the inner shapes converge uniformly to a piecewise linear function V of arbitrary slopes in [-1,1]. It is shown that the correlation kernels in the bulk…

New algorithms for efficient decoding of polar codes (which may be CRC-augmented), transmitted over either a binary erasure channel (BEC) or an additive white Gaussian noise channel (AWGNC), are presented. We start by presenting a new…

It is shown that polar codes achieve the symmetric capacity of discrete memoryless channels with arbitrary input alphabet sizes. It is shown that in general, channel polarization happens in several, rather than only two levels so that the…

We propose a new family of polar coding which realizes high coding gain, low complexity, and high throughput by introducing a protograph-based design. The proposed technique called as quasi-cyclic (QC) polar codes can be highly parallelized…

The positive operator valued localizations (POL) of a massive scalar boson are constructed and a characterization and structural analyses of their kernels are obtained. In the focus of this article are the causal features of the POL. There…

We establish a general framework for construction of small ensembles of capacity achieving linear codes for a wide range of (not necessarily memoryless) discrete symmetric channels, and in particular, the binary erasure and symmetric…