Sharif Digital Repository

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  

One of the categories of decoding techniques for DFT codes in erasure channels is the class of iterative algorithms. Iterative algorithms can be considered as kind of alternating mapping methods using the given information in a repetitive way. In this paper, we propose a new iterative method for decoding DFT codes. It will be shown that the proposed method outperforms me well-known methods such as Wiley/Marvasti, and ADPW methods in the decoding of DFT codes in erasure channels  

Averaging consensus on the values of nodes in a network is a principal problem in distributed computation. In the presence of erasure channels, conventional averaging consensus algorithms may not converge to the average value if packets are erased in arbitrary order. In this paper, we propose a 'Pseudo-Synchronous Averaging Consensus' (PSAC) algorithm to guarantee averaging consensus over erasure channels by employing tagged packets. We show that the PSAC algorithm has a simple structure and it can work with just two tags '0' and '1'. In asynchronous networks, the PSAC algorithm is a synchronizer in the sense that it keeps the updates of various nodes in step with each other. By exploiting... 

This paper presents a new technique for the state estimation and reference tracking of nonlinear dynamic systems over the packet erasure channel, which is an abstract model for transmission via the Internet, WiFi wireless network and ZigBee modules. A new encoder and decoder for real time state estimation of nonlinear dynamic systems at the end of communication link when the measurements are sent through the limited capacity erasure channel, are presented. Then, using the available results from control theory, a controller for reference tracking and hence the stability of the system is also designed. That is, for nonlinear systems, almost sure asymptotic state estimation and reference... 

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  

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  

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)... 

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... 

This paper presents a new technique for the state estimation and reference tracking of nonlinear dynamic systems over the packet erasure channel, which is an abstract model for transmission via the Internet, WiFi wireless network and ZigBee modules. A new encoder and decoder for real time state estimation of nonlinear dynamic systems at the end of communication link when the measurements are sent through the limited capacity erasure channel, are presented. Then, using the available results from control theory, a controller for reference tracking and hence the stability of the system is also designed. That is, for nonlinear systems, almost sure asymptotic state estimation and reference... 

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... 

The focus of the paper is on cross-layer transmission based on rateless coding for relay networks. In the proposed method, rateless coding is used at the packet level and a separate physical layer coding is used at the physical layer. As rateless codes are originally designed and optimized for erasure channels, using these codes at the physical layer can lead to significant performance degradation. The proposed scheme has the advantage of a cross-layer design which uses a rateless code at the packet level modeled by an erasure channel. Based on the analysis and simulation results provided in this paper, the cross-layer scheme results in earlier successful decoding at the destination  

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... 

This paper focuses on cross-layer transmission based on rateless coding for relay channels. In the proposed method, rateless coding is used at packet level and a separate physical layer coding is used at the physical layer. As rateless codes are originally designed and optimized for erasure channels, using these codes at the physical layer can lead to significant performance degradation. The proposed scheme has the advantage of a cross-layer design which uses a rateless code at the packet level modeled by an erasure channel. Based on the analysis and simulation results provided in this paper, there is an exact tradeoff between physical layer code rate and rateless code depth, and the optimum... 

This article addresses the stabilization of noiseless nonlinear dynamic systems over limited capacity communication channels. It is shown that the stability of nonlinear dynamic systems over memory-less communication channels implies an inequality condition between the Shannon channel capacity and the summation of the positive equilibrium Lyapunov exponents of the dynamic system or, equivalently, the logarithms of the magnitude of the unstable eigenvalues of system Jacobian. Furthermore, we propose an encoder, decoder, and a controller to prove that scalar nonlinear dynamic systems are stabilizable under the aforementioned inequality condition over the digital noiseless and the packet... 

The authors investigate the content distribution among the vehicles of a cluster in a vehicular ad-hoc network, exploiting network coding. The vehicles collaborate to disseminate the coded data packets, received from a roadside info-station based on IEEE 802.11 medium access control (MAC) protocol. Two types of network coding are considered: random linear network coding (RLNC) over a large finite field and random XORed network coding (RXNC). An analytical model is proposed to address the effect of random access MAC as well as the correlation among received coded packets on the performance of content distribution. First, a p-persistent carrier sense multiple access approximation for IEEE... 

This paper is concerned with the stability of linear time-invariant dynamic systems over the packet erasure channel subject to minimum bit rate constraint when an encoder and a decoder are unaware of the control signal. This assumption results in co-designing the encoder, decoder and controller. The encoder, decoder, controller and conditions relating transmission rate to packet erasure probability and eigenvalues of the system matrix A are presented for almost sure asymptotic stability of linear time-invariant dynamic systems over the packet erasure channel with feedback acknowledgment. When the eigenvalues of the system matrix A are real valued, it is shown that the obtained condition for... 

Remote observation of the state trajectory of nonlinear dynamic systems over limited capacity communication channels is studied. It is shown that two extreme cases are possible: Either the system is fully observable or the error in estimation blows up. The key observation is that such behavior is determined by the relationship between the Shannon capacity and the Lyapunov exponents; the well-known characterizing parameters of a communication channel on one side, and a dynamic system from the other side. In particular, it is proved that for nonlinear systems with initial state x0, the minimum capacity of an additive white Gaussian noise channel required for full observation of the system in... 

This paper presents a new technique for almost sure asymptotic state tracking, stability and reference tracking of nonlinear dynamic systems by remote controller over the packet erasure channel, which is an abstract model for transmission via WiFi and the Internet. By implementing a suitable linearization method, a proper encoder and decoder are presented for tracking the state trajectory of nonlinear systems at the end of communication link when the measurements are sent through the packet erasure channel. Then, a controller for reference tracking of the system is designed. In the proposed technique linearization is applied when the error between the states and an estimate of these states...