Sharif Digital Repository

Abstract. The linear sequential circuit approximation method for combiners with memory is used to find mutually correlated linear transforms of the input and output sequences in the well-known summation generator with any number of inputs. It is shown that the determined correlation coefficient is large enough for applying a fast correlation attack to the output sequence to reconstruct the initial states of the input linear feedback shift registers. The proposed attack is based on iterative probabilistic decoding and appropriately generated low-weight parity-checks. The required output sequence length and the computational complexity are both derived. Successful experimental results for the... 

We give an upper bound on the performance of the belief propagation algorithm in decoding a code over a binary-input output-symmetric channel in terms of the decoding threshold of the code over the erasure channel. Using this upper bound, we obtain the overhead of fountain codes on the erasure channel, provided that they are capacity-achieving on a symmetric channel. The upper bound is similar to a lower bound proved by Khandekar. The lower bound will be used to bound from above the reception overhead of fountain codes on symmetric channels  

The progressive-edge-growth (PEG) algorithm of Hu et al. is modified to improve the error floor performance of the constructed low-density parity-check (LDPC) codes. To improve the error floor, the original PEG algorithm is equipped with an efficient algorithm to find the dominant elementary trapping sets (ETS's) that are added to the Tanner graph of the under-construction code by the addition of each variable node and its adjacent edges. The aim is to select the edges, among the candidates available at each step of the original PEG algorithm, that prevent the creation of dominant ETS's. The proposed method is applicable to both regular and irregular variable node degree distributions.... 

In this paper, we consider the application of Low-Density Parity-Check (LDPC) codes in multi-carrier frequency-hopping (MC-FH) CDMA systems. We evaluate the performance of the coded system in a slowly Rayleigh fading frequency-selective channel using different construction methods of regular LDPC codes. We then compare the results with those of the Super-Orthogonal coded system. Our simulation results show that the LDPC coded scheme significantly outperforms the uncoded and the Super-Orthogonal coded scheme. Finally, we propose a new semi-random construction of regular LDPC code and evaluate its performance in MC-FH-CDMA system. Our numerical results indicate that this new construction... 

Recently, V. Sorokine et al. (see IEEE Trans. Commun., vol.48, no.10, p.1660-8, 2000; vol.48, no.11, p.1818-28, 2000) have introduced a class of low-density parity-check (LDPC) codes which, when applied on an IS-95 CDMA system, show, at BER=10-3, a five-fold and two-fold increase in capacity compared to the traditional uncoded scheme and to state-of-the-art low-rate orthogonal convolutional codes, respectively. However, these codes suffer from an error-floor at lower BERs which are needed for high-quality services, such as data. To enhance the capacity of CDMA systems, not only for moderate BER values but also for lower BER values, we modify the construction of these codes slightly, to... 

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)... 

We propose a new nonlinear Rao-Nam like symmetric key encryption scheme. In our design, we employ a specific type of coded modulation schemes namely quasi-cyclic low-density parity-check (QC-LDPC) lattice-codes which have low-complexity encoding and decoding algorithms. Due to the application of coded modulation schemes in our design, the proposed scheme performs encryption, encoding and modulation simultaneously. Therefore, we regard the proposed scheme as a joint cryptosystem. The proposed joint cryptosystem withstands all variants of chosen plaintext attacks applied on Rao-Nam like cryptosystems due to its nonlinearity. Moreover, some conditions implying the uniformity of the ciphertexts... 

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... 

We study the problem of transmission of binary input non-linear functions over a network of mobiles based on CDMA. Motivation for this study comes from the application of using cheap measurement devices installed on personal cellphones to monitor environmental parameters such as air pollution, temperature and noise level. Our model resembles the MAC model of Nazer and Gastpar except that the encoders are restricted to be CDMA encoders. Unlike the work of Nazer and Gastpar whose main attention is transmission of linear functions, we deal with non-linear functions with binary inputs. A main contribution of this paper is a lower bound on the computational capacity for this problem. While in the... 

We introduce a new secret-key cryptosystem based on 1-level QC-LDPC integer lattices. These lattices are practically implementable in high dimensions due to their low-complexity encoding and decoding algorithms. We exploit their efficient encoding and decoding algorithms to make a significant reduction in the complexity of lattice-based cryptosystems. Furthermore, the sparseness of the corresponding parity check matrix of 1-level QC-LDPC lattices and their good error performance, make them efficient choices in real world applications. In this paper, we propose a Rao-Nam like encryption scheme using 1-level QC-LDPC lattices. Some chosen-plaintext attacks and recent results on the Rao-Nam... 

We present a general purpose algorithm for finding low-weight codewords as well as for decoding a received codeword in any quasi-cyclic code whose length and dimension is a multiple of a power of 2. In this paper, we apply the algorithm on a McEliece variant recently proposed by Misoczki et al. (MDPC-McEliece: New McEliece variants from moderate density parity-check codes, 2013). In their paper, the authors present instances of LDPC codes with increased weight for use in a McEliece type PKC. They claim that all message-recovery and key-recovery attacks can be avoided. We show that this is not true for certain parameters and public-key matrices  

In this study, the authors introduce an efficient secure channel coding (joint cryptography-channel coding) scheme based on Latin square low-density lattice codes (Latin square LDLCs) over unconstrained power additive white Gaussian noise channel. They benefit the properties of Latin square LDLCs to dramatically reduce the key size of the proposed scheme while having an acceptable level of security compared with previous similar schemes. To reduce the key size, they consider two approaches: (i) saving the generating sequence of parity-check matrix of used Latin square LDLC as the part of secret key set; (ii) employing the Hermite normal form of the generator matrix of used Latin square LDLC... 

One of the approaches to modify the McEliece cryptosystem to overcome its large key size is replacing binary Goppa codes with a new structured code. However, this modification makes such cryptosystems encounter some new attacks. There are a few modified McEliece cryptosystem variants which are known to be secure. One of them is the cryptosystem introduced by Baldi et al. which uses quasi-cyclic low-density parity check (QC-LDPC) codes. This cryptosystem is still unbroken as no efficient attack has been reported against it since 2008. In this study, an attack has been applied to this cryptosystem which is feasible when the code length is a multiple of a power of 2. Also an important weakness... 

LDPC codes are deployed in many modern wired and wireless communication systems. while fully-parallel LDPC decoders are very efficient, they typically suffer from routing complexity. the split-row method effectively reduces this complexity with a minor performance loss. This paper shows the importance of symmetry in Split-Row architectures and proves that the implementation of Split-Row decoders based on new proposed smart column-permuted versions of parity check matrices leads to a better error performance as well as a more efficient hardware. Moreover, in order to achieve optimized column-permuted parity check matrices, a heuristic approach is proposed. This method is then generalized to... 

In this paper, the application of regular Low-Density Parity-Check (LDPC) codes in Multi-Carrier Frequency-Hopping (MC-FH) CDMA systems is studied. To this end, different well-known constructions of regular LDPC codes are considered and the performance of LDPC coded MC-FH-CDMA systems, based on these constructions, are evaluated and compared in a frequency-selective slowly Rayleigh fading channel. These results are compared with those previously reported for super-orthogonal convolutionally coded MC-FH-CDMA systems. The simulation results indicate that the LDPC coded MC-FH-CDMA system significantly outperforms the uncoded and super-orthogonal convolutionally coded schemes. To alleviate the... 

A secure channel coding (joint encryption-channel coding) scheme provides both data security and reliability in one combined process to achieve faster processing and/or more efficient implementation. The issue of using quasi-cyclic low-density parity-check (QC-LDPC) codes in a symmetric-key secure channel coding scheme is addressed. A set of this class of LDPC codes has recently been recommended by the NASA Goddard Space Flight Center for near-earth and deep-space communications. The proposed scheme provides an efficient error performance, an acceptable level of security and a low-complexity practicable implementation. The results indicate that the proposed scheme can efficiently employ... 

In this paper, we introduce a new family of lattices, namely QC-MDPC lattices which are a special case of LDPC lattices, and an improved bit flipping algorithm for decoding of these lattices. Encoding and decoding implementations of QC-MDPC lattices are practical in high dimensions. Indeed, to take advantage of practical decoding we use "Construction-A" lattices which makes a tight connection between the structure of lattices and codes. Using these features we design a lattice-based public key encryption scheme enjoying linear encryption and decryption complexities. The proposed scheme has a reasonable key size due to the sparseness of the parity-check matrix and the quasi cyclic structure...