Related papers: A Simple Proof of Fast Polarization
The polarization of light is critical in various applications, including quantum communication, where the photon polarization encoding a qubit can undergo uncontrolled changes when transmitted through optical fibers. Bends in the fiber,…
A reduced complexity sequential decoding algorithm for polar (sub)codes is described. The proposed approach relies on a decomposition of the polar (sub)code being decoded into a number of outer codes, and on-demand construction of codewords…
Polar codes have received increasing attention in the past decade, and have been selected for the next generation of wireless communication standard. Most research on polar codes has focused on codes constructed from a $2\times2$…
We prove two results on the universality of polar codes for source coding and channel communication. First, we show that for any polar code built for a source $P_{X,Z}$ there exists a slightly modified polar code - having the same rate, the…
We show how two circular polarization components of a linearly polarized pulse, propagating through a coherently driven dilute atomic vapor, can be well resolved in time domain by weak measurement. Slower group velocity of one of the…
Polarization in stars was first predicted by Chandrasekhar [1] who calculated a substantial linear polarization at the stellar limb for a pure electron-scattering atmosphere. This polarization will average to zero when integrated over a…
Polar coding over a class of binary discrete memoryless channels with channel knowledge at the encoder is studied. It is shown that polar codes achieve the capacity of convex and one-sided classes of symmetric channels.
The polar codes are proven to be capacity-achieving and are shown to have equivalent or even better finite-length performance than the turbo/LDPC codes under some improved decoding algorithms over the additive white Gaussian noise (AWGN)…
A challenging problem related to the design of polar codes is "robustness against channel parameter variations" as stated in Ar{\i}kan's original work. In this paper, we describe how the problem of robust polar code design can be viewed as…
We present a novel approach to precisely synthesize arbitrary polarization states of light with a high modulation bandwidth. Our approach consists of superimposing two laser light fields with the same wavelength, but with opposite circular…
A much simpler proof of Theorem 1 from M.Burnashev "Code spectrum and reliability function: Binary symmetric channel" is presented.
We consider two problems related to polar codes. First is the problem of polar codes construction and analysis of their performance without Monte-Carlo method. The formulas proposed are the same as those in [Mori-Tanaka], yet we believe…
Polar codes, introduced by Arikan, achieve symmetric capacity of any discrete memoryless channels under low encoding and decoding complexity. Recently, non-binary polar codes have been investigated. In this paper, we calculate error…
A method is proposed, called channel polarization, to construct code sequences that achieve the symmetric capacity $I(W)$ of any given binary-input discrete memoryless channel (B-DMC) $W$. The symmetric capacity is the highest rate…
A new score function is proposed for stack decoding of polar codes, which enables one to accurately compare paths of different lengths. The proposed score function includes bias, which reflects the average behaviour of the correct path.…
Polar codes are constructed for arbitrary channels by imposing an arbitrary quasigroup structure on the input alphabet. Just as with "usual" polar codes, the block error probability under successive cancellation decoding is…
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…
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…
The so-called {\it Modern Theory of Polarization}, which rigorously defines the spontaneous polarization of a period solid and provides a route for its computation in electronic structure codes through the Berry phase, is introduced in a…
Optical spectropolarimetry and broadband polarimetry in other wavebands has been a key to understanding many diverse aspects of AGN. In some cases polarization is due to synchrotron radiation, and in other cases it's due to scattering.…