An alternative proof of channel polarization for channels with arbitrary input alphabets

Guo, Jing; Sayir, Jossy; Qin, Minghai; Fàbregas, Albert Guillén i

doi:10.1109/allerton.2015.7447049

Cited by 2 publications

(4 citation statements)

References 8 publications

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“…Channel polarization is the primary polar code encoding process, which is a recursively implemented transformation, that generates N independent copies of any B-DMC where H i ð Þ N : 1 i N Likewise. The symmetric capacity value tends toward 0 or 1 when N is increased [20], [21]. This process is divided into two phases, the first one is channel combining phase and the second is channel splitting phase.…”

Section: Encoding Operationmentioning

confidence: 99%

Secured polar code derived from random hopped frozen-bits

2022

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The polar code is a unique coding approach that can achieve Shannon's capacity in modern communication systems' discrete memory-less channels with superior reliability, but it is not secure enough under modern attacks for such systems. This study aims to offer a comprehensive secured polar coding scheme that uses a combination of polar coding and the Mersenne-Twister pseudo-random number generator (MT-PRNG) to achieve a super secured encoding. The pre-shared crypto-system cyphering key initiates the starting state of the MT-PRNG as a seed. The randomly generated sequences govern the values of the frozen bits in polarized bit channels and their associated indices. A half-bit-error-rate probability system performance is calculated when the encoding ciphering keys at the receiver differ by a single bit from those utilized at the transmitter. Using calculated numerical analysis, the system is shown to be secure against brute force attacks, Rao-Nam attacks, and polar code reconstruction attacks.

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Section: Encoding Operationmentioning

confidence: 99%

Secured polar code derived from random hopped frozen-bits

2022

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“…, E m,n ) is an (m + 1)-dimensional random vector and E Sn n−1 := (E Sn r,n−1 : 0 ≤ r ≤ m). Namely, the random vector E n is recursively calculated by where the consideration is related to the study by Guo et al [6].…”

Section: Corollary 2 Consider the Polar Transformationmentioning

confidence: 99%

“…. , m and n ∈ N. Note that V n ≡ V (q) (E r,n : 0 ≤ r ≤ m) for n ∈ N 0 , where V n is defined in where the consideration is related to the study by Guo et al [6].…”

Section: B Second Part: Channelmentioning

confidence: 99%

“…The studies of q-ary polar codes are broadly divided into the following two approaches: The first approach is the strong polarization [9], [17], [18], i.e., the DMC is polarized to either noiseless or pure noisy channel. The second approach is the weak polarization [6], [10]- [12], [14], [16], i.e., the DMC is polarized to partially noiseless channels. The weak polarization is also called the multilevel polarization [10], [14], [16].…”

Section: Introductionmentioning

confidence: 99%

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A generalized erasure channel in the sense of polarization for binary erasure channels

Sakai

Iwata

2016

2016 IEEE Information Theory Workshop (ITW)

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The polar transformation of a binary erasure channel (BEC) can be exactly approximated by other BECs. Arıkan proposed that polar codes for a BEC can be efficiently constructed by using its useful property. This study proposes a new class of arbitrary input generalized erasure channels, which can be exactly approximated the polar transformation by other same channel models, as with the BEC. One of the main results is the recursive formulas of the polar transformation of the proposed channel. In the study, we evaluate the polar transformation by using the α-mutual information. Particularly, when the input alphabet size is a prime power, we examines the following: (i) inequalities for the average of the α-mutual information of the proposed channel after the one-step polar transformation, and (ii) the exact proportion of polarizations of the α-mutual information of proposed channels in infinite number of polar transformations.

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An alternative proof of channel polarization for channels with arbitrary input alphabets

Cited by 2 publications

References 8 publications

Secured polar code derived from random hopped frozen-bits

Secured polar code derived from random hopped frozen-bits

A generalized erasure channel in the sense of polarization for binary erasure channels

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