Unrestricted Kannada online handwritten akshara recognition using SDTW

In this paper, we present an unrestricted Kannada online handwritten character recognizer which is viable for real time applications. It handles Kannada and Indo-Arabic numerals, punctuation marks and special symbols like $, &, # etc, apart from all the aksharas of the Kannada script. The dataset used has handwriting of 69 people from four different locations, making the recognition writer independent. It was found that for the DTW classifier, using smoothed first derivatives as features, enhanced the performance to 89% as compared to preprocessed co-ordinates which gave 85%, but was too inefficient in terms of time. To overcome this, we used Statistical Dynamic Time Warping (SDTW) and achieved 46 times faster classification with comparable accuracy i.e. 88%, making it fast enough for practical applications. The accuracies reported are raw symbol recognition results from the classifier. Thus, there is good scope of improvement in actual applications. Where domain constraints such as fixed vocabulary, language models and post processing can be employed. A working demo is also available on tablet PC for recognition of Kannada words.

Comparison of HMM and SDTW for Tamil handwritten character recognition

In this paper, we compare the experimental results for Tamil online handwritten character recognition using HMM and Statistical Dynamic Time Warping (SDTW) as classifiers. HMM was used for a 156-class problem. Different feature sets and values for the HMM states & mixtures were tried and the best combination was found to be 16 states & 14 mixtures, giving an accuracy of 85%. The features used in this combination were retained and a SDTW model with 20 states and single Gaussian was used as classifier. Also, the symbol set was increased to include numerals, punctuation marks and special symbols like $, & and #, taking the number of classes to 188. It was found that, with a small addition to the feature set, this simple SDTW classifier performed on par with the more complicated HMM model, giving an accuracy of 84%. Mixture density estimation computations was reduced by 11 times. The recognition is writer independent, as the dataset used is quite large, with a variety of handwriting styles.

Abstract Characteristic Function

The characteristic function for a contraction is a classical complete unitary invariant devised by Sz.-Nagy and Foias. Just as a contraction is related to the Szego kernel k(S)(z, w) = ( 1 - z(w)over bar)- 1 for |z|, |w| < 1, by means of (1/k(S))( T, T *) = 0, we consider an arbitrary open connected domain Omega in C(n), a kernel k on Omega so that 1/k is a polynomial and a tuple T = (T(1), T(2), ... , T(n)) of commuting bounded operators on a complex separable Hilbert spaceHsuch that (1/k)( T, T *) >= 0. Under some standard assumptions on k, it turns out that whether a characteristic function can be associated with T or not depends not only on T, but also on the kernel k. We give a necessary and sufficient condition. When this condition is satisfied, a functional model can be constructed. Moreover, the characteristic function then is a complete unitary invariant for a suitable class of tuples T.

Full spin and spatial symmetry adapted technique for correlated electronic hamiltonians: Application to an icosahedral cluster

One of the long standing problems in quantum chemistry had been the inability to exploit full spatial and spin symmetry of an electronic Hamiltonian belonging to a non-Abelian point group. Here, we present a general technique which can utilize all the symmetries of an electronic (magnetic) Hamiltonian to obtain its full eigenvalue spectrum. This is a hybrid method based on Valence Bond basis and the basis of constant z-component of the total spin. This technique is applicable to systems with any point group symmetry and is easy to implement on a computer. We illustrate the power of the method by applying it to a model icosahedral half-filled electronic system. This model spans a huge Hilbert space (dimension 1,778,966) and in the largest non-Abelian point group. The C60 molecule has this symmetry and hence our calculation throw light on the higher energy excited states of the bucky ball. This method can also be utilized to study finite temperature properties of strongly correlated systems within an exact diagonalization approach. (C) 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012

Interference Alignment in Regenerating Codes for Distributed Storage: Necessity and Code Constructions

Regenerating codes are a class of recently developed codes for distributed storage that, like Reed-Solomon codes, permit data recovery from any arbitrary of nodes. However regenerating codes possess in addition, the ability to repair a failed node by connecting to any arbitrary nodes and downloading an amount of data that is typically far less than the size of the data file. This amount of download is termed the repair bandwidth. Minimum storage regenerating (MSR) codes are a subclass of regenerating codes that require the least amount of network storage; every such code is a maximum distance separable (MDS) code. Further, when a replacement node stores data identical to that in the failed node, the repair is termed as exact. The four principal results of the paper are (a) the explicit construction of a class of MDS codes for d = n - 1 >= 2k - 1 termed the MISER code, that achieves the cut-set bound on the repair bandwidth for the exact repair of systematic nodes, (b) proof of the necessity of interference alignment in exact-repair MSR codes, (c) a proof showing the impossibility of constructing linear, exact-repair MSR codes for d < 2k - 3 in the absence of symbol extension, and (d) the construction, also explicit, of high-rate MSR codes for d = k+1. Interference alignment (IA) is a theme that runs throughout the paper: the MISER code is built on the principles of IA and IA is also a crucial component to the nonexistence proof for d < 2k - 3. To the best of our knowledge, the constructions presented in this paper are the first explicit constructions of regenerating codes that achieve the cut-set bound.

Dilations of Gamma-contractions by solving operator equations

For a contraction P and a bounded commutant S of P. we seek a solution X of the operator equation S - S*P = (1 - P* P)(1/2) X (1 - P* P)(1/2) where X is a bounded operator on (Ran) over bar (1 - P* P)(1/2) with numerical radius of X being not greater than 1. A pair of bounded operators (S, P) which has the domain Gamma = {(z(1) + z(2), z(2)): vertical bar z(1)vertical bar < 1, vertical bar z(2)vertical bar <= 1} subset of C-2 as a spectral set, is called a P-contraction in the literature. We show the existence and uniqueness of solution to the operator equation above for a Gamma-contraction (S, P). This allows us to construct an explicit Gamma-isometric dilation of a Gamma-contraction (S, P). We prove the other way too, i.e., for a commuting pair (S, P) with parallel to P parallel to <= 1 and the spectral radius of S being not greater than 2, the existence of a solution to the above equation implies that (S, P) is a Gamma-contraction. We show that for a pure F-contraction (S, P), there is a bounded operator C with numerical radius not greater than 1, such that S = C + C* P. Any Gamma-isometry can be written in this form where P now is an isometry commuting with C and C. Any Gamma-unitary is of this form as well with P and C being commuting unitaries. Examples of Gamma-contractions on reproducing kernel Hilbert spaces and their Gamma-isometric dilations are discussed. (C) 2012 Elsevier Inc. All rights reserved.

Receive Antenna Selection for Time-Varying Channels Using Discrete Prolate Spheroidal Sequences

Receive antenna selection (AS) has been shown to maintain the diversity benefits of multiple antennas while potentially reducing hardware costs. However, the promised diversity gains of receive AS depend on the assumptions of perfect channel knowledge at the receiver and slowly time-varying fading. By explicitly accounting for practical constraints imposed by the next-generation wireless standards such as training, packetization and antenna switching time, we propose a single receive AS method for time-varying fading channels. The method exploits the low training overhead and accuracy possible from the use of discrete prolate spheroidal (DPS) sequences based reduced rank subspace projection techniques. It only requires knowledge of the Doppler bandwidth, and does not require detailed correlation knowledge. Closed-form expressions for the channel prediction and estimation error as well as symbol error probability (SEP) of M-ary phase-shift keying (MPSK) for symbol-by-symbol receive AS are also derived. It is shown that the proposed AS scheme, after accounting for the practical limitations mentioned above, outperforms the ideal conventional single-input single-output (SISO) system with perfect CSI and no AS at the receiver and AS with conventional estimation based on complex exponential basis functions.

Local demodulation of holograms using the Riesz transform with application to microscopy

We propose a Riesz transform approach to the demodulation of digital holograms. The Riesz transform is a higher-dimensional extension of the Hilbert transform and is steerable to a desired orientation. Accurate demodulation of the hologram requires a reliable methodology by which quadrature-phase functions (or simply, quadratures) can be constructed. The Riesz transform, by itself, does not yield quadratures. However, one can start with the Riesz transform and construct the so-called vortex operator by employing the notion of quasi-eigenfunctions, and this approach results in accurate quadratures. The key advantage of using the vortex operator is that it effectively handles nonplanar fringes (interference patterns) and has the ability to compensate for the local orientation. Therefore, this method results in aberration-free holographic imaging even in the case when the wavefronts are not planar. We calibrate the method by estimating the orientation from a reference hologram, measured with an empty field of view. Demodulation results on synthesized planar as well as nonplanar fringe patterns show that the accuracy of demodulation is high. We also perform validation on real experimental measurements of Caenorhabditis elegans acquired with a digital holographic microscope. (c) 2012 Optical Society of America

Frequency domain turbo equalization for MIMO-CPSC systems with large delay spreads

In this paper, we consider low-complexity turbo equalization for multiple-input multiple-output (MIMO) cyclic prefixed single carrier (CPSC) systems in MIMO inter-symbol interference (ISI) channels characterized by large delay spreads. A low-complexity graph based equalization is carried out in the frequency domain. Because of the reduction in correlation among the noise samples that happens for large frame sizes and delay spreads in frequency domain processing, improved performance compared to time domain processing is shown to be achieved. This improved performance is attractive for equalization in severely delay spread ISI channels like ultrawideband channels and underwater acoustic channels.

Generalizing the Amplify-and-Forward Relay Gain Model: An Optimal SEP Perspective

Two models for AF relaying, namely, fixed gain and fixed power relaying, have been extensively studied in the literature given their ability to harness spatial diversity. In fixed gain relaying, the relay gain is fixed but its transmit power varies as a function of the source-relay channel gain. In fixed power relaying, the relay transmit power is fixed, but its gain varies. We revisit and generalize the fundamental two-hop AF relaying model. We present an optimal scheme in which an average power constrained AF relay adapts its gain and transmit power to minimize the symbol error probability (SEP) at the destination. Also derived are insightful and practically amenable closed-form bounds for the optimal relay gain. We then analyze the SEP of MPSK, derive tight bounds for it, and characterize the diversity order for Rayleigh fading. Also derived is an SEP approximation that is accurate to within 0.1 dB. Extensive results show that the scheme yields significant energy savings of 2.0-7.7 dB at the source and relay. Optimal relay placement for the proposed scheme is also characterized, and is different from fixed gain or power relaying. Generalizations to MQAM and other fading distributions are also discussed.

The defect sequence for contractive tuples

We introduce the defect sequence for a contractive tuple of Hilbert space operators and investigate its properties. The defect sequence is a sequence of numbers, called defect dimensions associated with a contractive tuple. We show that there are upper bounds for the defect dimensions. The tuples for which these upper bounds are obtained, are called maximal contractive tuples. The upper bounds are different in the non-commutative and in the commutative case. We show that the creation operators on the full Fock space and the coordinate multipliers on the Drury-Arveson space are maximal. We also study pure tuples and see how the defect dimensions play a role in their irreducibility. (C) 2012 Elsevier Inc. All rights reserved.

Secure Computation in a Bidirectional Relay

Bidirectional relaying, where a relay helps two user nodes to exchange equal length binary messages, has been an active area of recent research. A popular strategy involves a modified Gaussian MAC, where the relay decodes the XOR of the two messages using the naturally-occurring sum of symbols simultaneously transmitted by user nodes. In this work, we consider the Gaussian MAC in bidirectional relaying with an additional secrecy constraint for protection against a honest but curious relay. The constraint is that, while the relay should decode the XOR, it should be fully ignorant of the individual messages of the users. We exploit the symbol addition that occurs in a Gaussian MAC to design explicit strategies that achieve perfect independence between the received symbols and individual transmitted messages. Our results actually hold for a more general scenario where the messages at the two user nodes come from a finite Abelian group G, and the relay must decode the sum within G of the two messages. We provide a lattice coding strategy and study optimal rate versus average power trade-offs for asymptotically large dimensions.

Optimal Linear Codes with a Local-Error-Correction Property

Motivated by applications to distributed storage, Gopalan et al recently introduced the interesting notion of information-symbol locality in a linear code. By this it is meant that each message symbol appears in a parity-check equation associated with small Hamming weight, thereby enabling recovery of the message symbol by examining a small number of other code symbols. This notion is expanded to the case when all code symbols, not just the message symbols, are covered by such ``local'' parity. In this paper, we extend the results of Gopalan et. al. so as to permit recovery of an erased code symbol even in the presence of errors in local parity symbols. We present tight bounds on the minimum distance of such codes and exhibit codes that are optimal with respect to the local error-correction property. As a corollary, we obtain an upper bound on the minimum distance of a concatenated code.

DMT-optimal, Low ML-Complexity STBC-Schemes for Asymmetric MIMO Systems

For an n(t) transmit, nr receive antenna (n(t) x n(r)) MIMO system with quasi- static Rayleigh fading, it was shown by Elia et al. that space-time block code-schemes (STBC-schemes) which have the non-vanishing determinant (NVD) property and are based on minimal-delay STBCs (STBC block length equals n(t)) with a symbol rate of n(t) complex symbols per channel use (rate-n(t) STBC) are diversity-multiplexing gain tradeoff (DMT)-optimal for arbitrary values of n(r). Further, explicit linear STBC-schemes (LSTBC-schemes) with the NVD property were also constructed. However, for asymmetric MIMO systems (where n(r) < n(t)), with the exception of the Alamouti code-scheme for the 2 x 1 system and rate-1, diagonal STBC-schemes with NVD for an nt x 1 system, no known minimal-delay, rate-n(r) LSTBC-scheme has been shown to be DMT-optimal. In this paper, we first obtain an enhanced sufficient criterion for an STBC-scheme to be DMT optimal and using this result, we show that for certain asymmetric MIMO systems, many well-known LSTBC-schemes which have low ML-decoding complexity are DMT-optimal, a fact that was unknown hitherto.

Field extension code based dispersion matrices for coherently detected space-time shift keying

Motivated by the recent Coherent Space-Time Shift Keying (CSTSK) philosophy, we construct new dispersion matrices for rotationally invariant PSK signaling sets. Given a specific PSK signal constellation, the dispersion matrices of the existing CSTSK scheme were chosen by maximizing the mutual information over randomly generated sets of dispersion matrices. In this contribution we propose a general method for constructing a set of structured dispersion matrices for arbitrary PSK signaling sets using Field Extension (FE) codes and then study the attainable Symbol Error Rate (SER) performance of some example constructions. We demonstrate that the proposed dispersion scheme is capable of outperforming the existing dispersion arrangement at medium to high SNRs.