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Item Open Access Binary sequences with low aperiodic autocorrelation for synchronization purposes(IEEE, 2003) Kocabaş, Ş. E.; Atalar, AbdullahShow more An evolutionary algorithm is used to find three sets of binary sequences of length 49-100 suitable for the synchronization of digital communication systems. Optimization of the sets are done by taking into consideration the type of preamble used in data frames and the phase-lock mechanism of the communication system. The preamble is assumed to be either a pseudonoise (PN) sequence or a sequence of 1's. There may or may not be phase ambiguity in detection. With this categorization, the first set of binary sequences is optimized with respect to aperiodic autocorrelation which corresponds to the random (PN) preamble without phase ambiguity case. The second and third sets are optimized with respect to a modified aperiodic autocorrelation for different figures of merit corresponding to the predetermined preamble (sequence of 1's) with and without phase ambiguity cases.Show more Item Open Access Bounds on the capacity of random insertion and deletion-additive noise channels(IEEE, 2013) Rahmati, M.; Duman, T. M.Show more We develop several analytical lower bounds on the capacity of binary insertion and deletion channels by considering independent uniformly distributed (i.u.d.) inputs and computing lower bounds on the mutual information between the input and output sequences. For the deletion channel, we consider two different models: i.i.d. deletion-substitution channel and i.i.d. deletion channel with additive white Gaussian noise (AWGN). These two models are considered to incorporate effects of the channel noise along with the synchronization errors. For the insertion channel case, we consider Gallager's model in which the transmitted bits are replaced with two random bits and uniform over the four possibilities independently of any other insertion events. The general approach taken is similar in all cases, however the specific computations differ. Furthermore, the approach yields a useful lower bound on the capacity for a wide range of deletion probabilities of the deletion channels, while it provides a beneficial bound only for small insertion probabilities (less than 0.25) of the insertion model adopted. We emphasize the importance of these results by noting that: 1) our results are the first analytical bounds on the capacity of deletion-AWGN channels, 2) the results developed are the best available analytical lower bounds on the deletion-substitution case, 3) for the Gallager insertion channel model, the new lower bound improves the existing results for small insertion probabilities. © 1963-2012 IEEE.Show more Item Open Access Channel polarization: A method for constructing capacity-achieving codes(IEEE, 2008-07) Arıkan, ErdalShow more 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 I(W) is the highest rate achievable subject to using the input letters of the channel equiprobably and equals the capacity C(W) if the channel has certain symmetry properties. Channel polarization refers to the fact that it is possible to synthesize, out of N independent copies of a given B-DMC W, a different set of N binary-input channels such that the capacities of the latter set, except for a negligible fraction of them, are either near 1 or near 0. This second set of N channels are well-conditioned for channel coding: one need only send data at full rate through channels with capacity near 1 and at 0 rate through the others. The main coding theorem about polar coding states that, given any B-DMC W with I(W) > 0 and any fixed 0 < δ < I(W), there exist finite constants n1 (W, δ) and c(W, δ) such that for all n ≥ n1, there exist polar codes with block length N = 2n, rate R > I(W)-δ, and probability of block decoding error Pe ≤ cN-1/4. The codes with this performance can be encoded and decoded within complexity O(N log N). © 2008 IEEE.Show more Item Open Access Channel polarization: a method for constructing capacity-achieving codes for symmetric binary-input memoryless channels(IEEE, 2009) Arikan, E.Show more 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 achievable subject to using the input letters of the channel with equal probability. Channel polarization refers to the fact that it is possible to synthesize, out of N independent copies of a given B-DMC W, a second set of N binary-input channels {WN (i): 1 ≤ i ≤ N} becomes large, the fraction of indices i for which I(WN (i) is near 1 approaches I(W) and the fraction for which I(WN (i) is near 0 approaches 1 - I(W). The polarized channels WN (i) are well-conditioned for channel coding: one need only send data at rate 1 through those with capacity near 1 and at rate 0 through the remaining. Codes constructed on the basis of this idea are called polar codes. The paper proves that, given any B-DMC W with I(W) and any target rate R < I(W), there exists a sequence of polar codes {Cn;n ≥ 1 such that Cn has block-length N = 2n, rate ≥ R, and probability of block error under successive cancellation decoding bounded as Pe (N, R) ≤ O(N-1/4 independently of the code rate. This performance is achievable by encoders and decoders with complexity O(N\log N) for each.Show more Item Open Access Counting surrounding nodes using DS-SS signals and de Bruijn sequences in blind environment(IEEE, 2013-03) Warty, C.; Seçer, Görkem; Yu, R.W.; Spinsante, S.Show more In recent years the technological development has encouraged several applications based on node to node communications without any fixed infrastructure. This paper presents preliminary evaluation of popular estimating techniques to populate active nodes in the neighborhood using De Bruijn sequences. They have much higher cardinality compared to any other family of binary sequences at a parity of length. This characteristic of De Bruijn sequences can be exploited to identify the presence of an active node in a dense surrounding, to assist the primary node in making intelligent decisions in a blind or foggy environment. The simulation model in this paper evaluates the use of eigenvalue estimation to estimate the spreading sequence among noisy signals, based on eigenvalues analysis techniques. The received signal is divided into windows, from which a covariance matrix is computed; the sequence can be reconstructed from the two first eigenvectors of this matrix, and that useful information, such as the desynchronization time, can be extracted from the eigenvalues. © 2013 IEEE.Show more Item Open Access Energy minimizing vehicle routing problem(Springer, 2007) Kara, İ.; Kara, Bahar Y.; Yetiş, M. K.Show more This paper proposes a new cost function based on distance and load of the vehicle for the Capacitated Vehicle Routing Problem. The vehicle-routing problem with this new load-based cost objective is called the Energy Minimizing Vehicle Routing Problem (EMVRP). Integer linear programming formulations with O(n 2) binary variables and O(n2) constraints are developed for the collection and delivery cases, separately. The proposed models are tested and illustrated by classical Capacitated Vehicle Routing Problem (CVRP) instances from the literature using CPLEX 8.0.Show more Item Open Access On Lempel-Ziv complexity of sequences(Springer, Berlin, Heidelberg, 2006) Doǧanaksoy, A.; Göloǧlu, FarukShow more We derive recurrences for counting the number a(n, r) of sequences of length n with Lempel-Ziv complexity r, which has important applications, for instance testing randomness of binary sequences. We also give algorithms to compute these recurrences. We employed these algorithms to compute a(n, r) and expected value. EPn, of number of patterns of a sequence of length n, for relatively large n. We offer a randomness test based on the algorithms to be used for testing randomness of binary sequences. We give outputs of the algorithms for some n. We also provide results of the proposed test applied to the outputs of contestant stream ciphers of ECRYPT's eSTREAM. © Springer-Verlag Berlin Heidelberg 2006.Show more