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binary-erasure-channel
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On the scaling of polar codes: II. the behavior of un-polarized channels
, Article IEEE International Symposium on Information Theory - Proceedings, 13 June 2010 through 18 June 2010, Austin, TX ; 2010 , Pages 879-883 ; 21578103 (ISSN) ; 9781424469604 (ISBN) ; Alishahi, K ; Urbanke, R ; Sharif University of Technology
2010
Abstract
We provide upper and lower bounds on the escape rate of the Bhattacharyya process corresponding to polar codes where transmission takes place over the the binary erasure channel. More precisely, we bound the exponent of the number of sub-channels whose Bhattacharyya constant falls in a fixed interval [a, b]. Mathematically this can be stated as bounding the limit limn →∞ 1/n ln ℙ(Zn ∈ [a,b]), where Z n is the Bhattacharyya process. The quantity ℙ (Zn ∈ [a,b]) represents the fraction of sub-channels that are still un-polarized at time n
Secret key cryptosystem based on polar codes over Binary Erasure Channel
, Article 2013 10th International ISC Conference on Information Security and Cryptology, ISCISC 2013 ; 2013 ; Shooshtari, M. K ; Aref, M. R ; Sharif University of Technology
2013
Abstract
This paper proposes an efficient secret key cryptosystem based on polar codes over Binary Erasure Channel. We introduce a method, for the first time to our knowledge, to hide the generator matrix of the polar codes from an attacker. In fact, our main goal is to achieve secure and reliable communication using finite-length polar codes. The proposed cryptosystem has a significant security advantage against chosen plaintext attacks in comparison with the Rao-Nam cryptosystem. Also, the key length is decreased after applying a new compression algorithm. Moreover, this scheme benefits from high code rate and proper error performance for reliable communication
Universal bounds on the scaling behavior of polar codes
, Article IEEE International Symposium on Information Theory - Proceedings ; 2012 , Pages 1957-1961 ; 9781467325790 (ISBN) ; Hassani, S. H ; Urbanke, R ; Sharif University of Technology
IEEE
2012
Abstract
We consider the problem of determining the tradeoff between the rate and the block-length of polar codes for a given block error probability when we use the successive cancellation decoder. We take the sum of the Bhattacharyya parameters as a proxy for the block error probability, and show that there exists a universal parameter μ such that for any binary memoryless symmetric channel W with capacity I(W), reliable communication requires rates that satisfy R < I(W) - αN -1/μ, where α is a positive constant and N is the block-length. We provide lower bounds on μ, namely μ ≥ 3.553, and we conjecture that indeed μ = 3.627, the parameter for the binary erasure channel
New sequences of capacity achieving LDPC code ensembles over the binary erasure channel
, Article IEEE Transactions on Information Theory ; Volume 56, Issue 12 , 2010 , Pages 6332-6346 ; 00189448 (ISSN) ; Banihashemi, A. H ; Sharif University of Technology
2010
Abstract
In this paper, new sequences (λn,ρn) of capacity achieving low-density parity-check (LDPC) code ensembles over the binary erasure channel (BEC) is introduced. These sequences include the existing sequences by Shokrollahi as a special case. For a fixed code rate R, in the set of proposed sequences, Shokrollahi's sequences are superior to the rest of the set in that for any given value of n, their threshold is closer to the capacity upper bound 1 - R. For any given δ, 0 < δ < 1 - R, however, there are infinitely many sequences in the set that are superior to Shokrollahi's sequences in that for each of them, there exists an integer number n0, such that for any n > n0, the sequence (λn, ρn)...
A multi-layer encoding and decoding strategy for binary erasure channel
, Article IEEE Transactions on Information Theory ; Volume 65, Issue 7 , 2019 , Pages 4143-4151 ; 00189448 (ISSN) ; Aref, M. R ; Sharif University of Technology
Institute of Electrical and Electronics Engineers Inc
2019
Abstract
In this paper, we consider a binary erasure channel (BEC) with an unknown erasure probability of {delta } at a transmitter. In addition, we consider that {delta } has a constant value in each transmission block and the transmitter knows the probability distribution of {delta }. For this problem with the infinite block length, based on the distribution of the random variable {delta } , a multi-layer encoding strategy at the transmitter and a successive decoding strategy at the receiver are proposed. In our proposed scheme, based on the value of {delta } , the receiver can decode a part of transmitted data from different transmission layers. In order to have a comparison with other erasure...
Capacity achieving linear codes with random binary sparse generating matrices over the binary symmetric channel
, Article IEEE International Symposium on Information Theory - Proceedings ; 2012 , Pages 621-625 ; 9781467325790 (ISBN) ; Abadi, H. K ; Pad, P ; Saeedi, H ; Marvasti, F ; Alishahi, K ; Sharif University of Technology
IEEE
2012
Abstract
In this paper, we prove the existence of capacity achieving linear codes with random binary sparse generating matrices over the Binary Symmetric Channel (BSC). The results on the existence of capacity achieving linear codes in the literature are limited to the random binary codes with equal probability generating matrix elements and sparse parity-check matrices. Moreover, the codes with sparse generating matrices reported in the literature are not proved to be capacity achieving for channels other than Binary Erasure Channel. As opposed to the existing results in the literature, which are based on optimal maximum a posteriori decoders, the proposed approach is based on a different decoder...
Secret key cryptosystem based on non-systematic polar codes
, Article Wireless Personal Communications ; Volume 84, Issue 2 , September , 2015 , Pages 1345-1373 ; 09296212 (ISSN) ; Aref, M. R ; Eghlidos, T ; Sharif University of Technology
Springer New York LLC
2015
Abstract
Polar codes are a new class of error correcting linear block codes, whose generator matrix is specified by the knowledge of transmission channel parameters, code length and code dimension. Moreover, regarding computational security, it is assumed that an attacker with a restricted processing power has unlimited access to the transmission media. Therefore, the attacker can construct the generator matrix of polar codes, especially in the case of binary erasure channels, on which this matrix can be easily constructed. In this paper, we introduce a novel method to keep the generator matrix of polar codes in secret in a way that the attacker cannot access the required information to decode the...