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.

An Adaptive Conditional Zero-Forcing Decoder With Full-Diversity, Least Complexity and Essentially-ML Performance for STBCs

A low complexity, essentially-ML decoding technique for the Golden code and the three antenna Perfect code was introduced by Sirianunpiboon, Howard and Calderbank. Though no theoretical analysis of the decoder was given, the simulations showed that this decoding technique has almost maximum-likelihood (ML) performance. Inspired by this technique, in this paper we introduce two new low complexity decoders for Space-Time Block Codes (STBCs)-the Adaptive Conditional Zero-Forcing (ACZF) decoder and the ACZF decoder with successive interference cancellation (ACZF-SIC), which include as a special case the decoding technique of Sirianunpiboon et al. We show that both ACZF and ACZF-SIC decoders are capable of achieving full-diversity, and we give a set of sufficient conditions for an STBC to give full-diversity with these decoders. We then show that the Golden code, the three and four antenna Perfect codes, the three antenna Threaded Algebraic Space-Time code and the four antenna rate 2 code of Srinath and Rajan are all full-diversity ACZF/ACZF-SIC decodable with complexity strictly less than that of their ML decoders. Simulations show that the proposed decoding method performs identical to ML decoding for all these five codes. These STBCs along with the proposed decoding algorithm have the least decoding complexity and best error performance among all known codes for transmit antennas. We further provide a lower bound on the complexity of full-diversity ACZF/ACZF-SIC decoding. All the five codes listed above achieve this lower bound and hence are optimal in terms of minimizing the ACZF/ACZF-SIC decoding complexity. Both ACZF and ACZF-SIC decoders are amenable to sphere decoding implementation.

Low complexity adaptation for channel shortening equalizers

Since the days of Digital Subscriber Links(DSL), Time Domain Equalizers(TEQ's) have been used to combat time dispersive channels in Multicarrier Systems. In this paper, we propose computationally inexpensive techniques to recompute TEQ weights in the presence of changes in the channel, especially over fast fading channels. The techniques use no extra information except the perturbation itself, and provide excellent approximations to the new TEQ weights. The proposed adaptation techniques are shown to perform admirably well for small changes in channels for OFDM systems.

Minimizing the complexity of fast sphere decoding of STBCs

Decoding of linear space-time block codes (STBCs) with sphere-decoding (SD) is well known. A fast-version of the SD known as fast sphere decoding (FSD) has been recently studied by Biglieri, Hong and Viterbo. Viewing a linear STBC as a vector space spanned by its defining weight matrices over the real number field, we define a quadratic form (QF), called the Hurwitz-Radon QF (HRQF), on this vector space and give a QF interpretation of the FSD complexity of a linear STBC. It is shown that the FSD complexity is only a function of the weight matrices defining the code and their ordering, and not of the channel realization (even though the equivalent channel when SD is used depends on the channel realization) or the number of receive antennas. It is also shown that the FSD complexity is completely captured into a single matrix obtained from the HRQF. Moreover, for a given set of weight matrices, an algorithm to obtain a best ordering of them leading to the least FSD complexity is presented. The well known classes of low FSD complexity codes (multi-group decodable codes, fast decodable codes and fast group decodable codes) are presented in the framework of HRQF.

Sharp raman anomalies and broken adiabaticity at a pressure induced transition from band to topological insulator in Sb2Se3

The nontrivial electronic topology of a topological insulator is thus far known to display signatures in a robust metallic state at the surface. Here, we establish vibrational anomalies in Raman spectra of the bulk that signify changes in electronic topology: an E-g(2) phonon softens unusually and its linewidth exhibits an asymmetric peak at the pressure induced electronic topological transition (ETT) in Sb2Se3 crystal. Our first-principles calculations confirm the electronic transition from band to topological insulating state with reversal of parity of electronic bands passing through a metallic state at the ETT, but do not capture the phonon anomalies which involve breakdown of adiabatic approximation due to strongly coupled dynamics of phonons and electrons. Treating this within a four-band model of topological insulators, we elucidate how nonadiabatic renormalization of phonons constitutes readily measurable bulk signatures of an ETT, which will facilitate efforts to develop topological insulators by modifying a band insulator. DOI: 10.1103/PhysRevLett.110.107401

The evolution of complexity in social organization-A model using dominance-subordinate behavior in two social wasp species

Dominance and subordinate behaviors are important ingredients in the social organizations of group living animals. Behavioral observations on the two eusocial species Ropalidia marginata and Ropalidia cyathiformis suggest varying complexities in their social systems. The queen of R. cyathiformis is an aggressive individual who usually holds the top position in the dominance hierarchy although she does not necessarily show the maximum number of acts of dominance, while the R. marginata queen rarely shows aggression and usually does not hold the top position in the dominance hierarchy of her colony. In R. marginata, more workers are involved in dominance-subordinate interactions as compared to R. cyathiformis. These differences are reflected in the distribution of dominance-subordinate interactions among the hierarchically ranked individuals in both the species. The percentage of dominance interactions decreases gradually with hierarchical ranks in R. marginata while in R. cyathiformis it first increases and then decreases. We use an agent-based model to investigate the underlying mechanism that could give rise to the observed patterns for both the species. The model assumes, besides some non-interacting individuals, the interaction probabilities of the agents depend on their pre-differentiated winning abilities. Our simulations show that if the queen takes up a strategy of being involved in a moderate number of dominance interactions, one could get the pattern similar to R. cyathiformis, while taking up the strategy of very low interactions by the queen could lead to the pattern of R. marginata. We infer that both the species follow a common interaction pattern, while the differences in their social organization are due to the slight changes in queen as well as worker strategies. These changes in strategies are expected to accompany the evolution of more complex societies from simpler ones.

Performance improvement of short-length regular low-density parity-check codes with low-complexity post-processing

It is well known that extremely long low-density parity-check (LDPC) codes perform exceptionally well for error correction applications, short-length codes are preferable in practical applications. However, short-length LDPC codes suffer from performance degradation owing to graph-based impairments such as short cycles, trapping sets and stopping sets and so on in the bipartite graph of the LDPC matrix. In particular, performance degradation at moderate to high E-b/N-0 is caused by the oscillations in bit node a posteriori probabilities induced by short cycles and trapping sets in bipartite graphs. In this study, a computationally efficient algorithm is proposed to improve the performance of short-length LDPC codes at moderate to high E-b/N-0. This algorithm makes use of the information generated by the belief propagation (BP) algorithm in previous iterations before a decoding failure occurs. Using this information, a reliability-based estimation is performed on each bit node to supplement the BP algorithm. The proposed algorithm gives an appreciable coding gain as compared with BP decoding for LDPC codes of a code rate equal to or less than 1/2 rate coding. The coding gains are modest to significant in the case of optimised (for bipartite graph conditioning) regular LDPC codes, whereas the coding gains are huge in the case of unoptimised codes. Hence, this algorithm is useful for relaxing some stringent constraints on the graphical structure of the LDPC code and for developing hardware-friendly designs.

Transport across a junction of topological insulators and a superconductor

We study transport across a line junction lying between two orthogonal topological insulator surfaces and a superconductor which can have either s-wave (spin-singlet) or p-wave (spin-triplet) pairing symmetry. The junction can have three time-reversal invariant barriers on three sides. We compute the charge and the spin conductance across such a junction and study their behaviors as a function of the bias voltage applied across the junction and the three parameters used to characterize the barrier. We find that the presence of topological insulators and a superconductor leads to both Dirac- and Schrodinger-like features in charge and spin conductances. We discuss the effect of bound states on the superconducting side of the barrier on the conductance; in particular, we show that for triplet p-wave superconductors, such a junction may be used to determine the spin state of its Cooper pairs. Our study reveals that there is a nonzero spin conductance for some particular spin states of the triplet Cooper pairs; this is an effect of the topological insulators which break the spin rotation symmetry. Finally, we find an unusual satellite peak (in addition to the usual zero bias peak) in the spin conductance for p-wave symmetry of the superconductor order parameter.

Reduced-complexity partial-interference-cancellation group decoder for STBCs

In this letter, we propose a reduced-complexity implementation of partial interference cancellation group decoder with successive interference cancellation (PIC-GD-SIC) by employing the theory of displacement structures. The proposed algorithm exploits the block-Toeplitz structure of the effective matrix and chooses an ordering of the groups such that the zero-forcing matrices associated with the various groups are obtained through Schur recursions without any approximations. We show using an example that the proposed implementation offers a significantly reduced computational complexity compared to the direct approach without any loss in performance.

On the sphere decoding complexity of high-rate multigroup decodable STBCs in asymmetric MIMO systems

A space-time block code (STBC) is said to be multigroup decodable if the information symbols encoded by it can be partitioned into two or more groups such that each group of symbols can be maximum-likelihood (ML) decoded independently of the other symbol groups. In this paper, we show that the upper triangular matrix encountered during the sphere decoding of a linear dispersion STBC can be rank-deficient even when the rate of the code is less than the minimum of the number of transmit and receive antennas. We then show that all known families of high-rate (rate greater than 1) multigroup decodable codes have rank-deficient matrix even when the rate is less than the number of transmit and receive antennas, and this rank-deficiency problem arises only in asymmetric MIMO systems when the number of receive antennas is strictly less than the number of transmit antennas. Unlike the codes with full-rank matrix, the complexity of the sphere decoding-based ML decoder for STBCs with rank-deficient matrix is polynomial in the constellation size, and hence is high. We derive the ML sphere decoding complexity of most of the known high-rate multigroup decodable codes, and show that for each code, the complexity is a decreasing function of the number of receive antennas.

Topological saliency

Topological methods have been successfully used to identify features in scalar fields and to measure their importance. In this paper, we define a notion of topological saliency that captures the relative importance of a topological feature with respect to other features in its local neighborhood. Features are identified by extreme points of an input scalar field, and their importance measured by the so-called topological persistence. Computing the topological saliency of all features for varying neighborhood sizes results in a saliency plot that serves as a summary of relative importance of all topological features. We develop a convenient tool for users to interactively select and inspect features using the saliency plot. We demonstrate the use of topological saliency together with the rich information encoded in the saliency plot in several applications, including key feature identification, scalar field simplification, and feature clustering. (C) 2013 Elsevier Ltd. All rights reserved.

Floquet generation of Majorana end modes and topological invariants

We show how Majorana end modes can be generated in a one-dimensional system by varying some of the parameters in the Hamiltonian periodically in time. The specific model we consider is a chain containing spinless electrons with a nearest-neighbor hopping amplitude, a p-wave superconducting term, and a chemical potential; this is equivalent to a spin-1/2 chain with anisotropic XY couplings between nearest neighbors and a magnetic field applied in the (z) over cap direction. We show that varying the chemical potential (or magnetic field) periodically in time can produce Majorana modes at the ends of a long chain. We discuss two kinds of periodic driving, periodic delta-function kicks, and a simple harmonic variation with time. We discuss some distinctive features of the end modes such as the inverse participation ratio of their wave functions and their Floquet eigenvalues which are always equal to +/- 1 for time-reversal-symmetric systems. For the case of periodic delta-function kicks, we use the effective Hamiltonian of a system with periodic boundary conditions to define two topological invariants. The first invariant is a well-known winding number, while the second invariant has not appeared in the literature before. The second invariant is more powerful in that it always correctly predicts the numbers of end modes with Floquet eigenvalues equal to + 1 and -1, while the first invariant does not. We find that the number of end modes can become very large as the driving frequency decreases. We show that periodic delta-function kicks in the hopping and superconducting terms can also produce end modes. Finally, we study the effect of electron-phonon interactions (which are relevant at finite temperatures) and a random noise in the chemical potential on the Majorana modes.

Construction of Block Orthogonal STBCs and Reducing Their Sphere Decoding Complexity

Construction of high rate Space Time Block Codes (STBCs) with low decoding complexity has been studied widely using techniques such as sphere decoding and non Maximum-Likelihood (ML) decoders such as the QR decomposition decoder with M paths (QRDM decoder). Recently Ren et al., presented a new class of STBCs known as the block orthogonal STBCs (BOSTBCs), which could be exploited by the QRDM decoders to achieve significant decoding complexity reduction without performance loss. The block orthogonal property of the codes constructed was however only shown via simulations. In this paper, we give analytical proofs for the block orthogonal structure of various existing codes in literature including the codes constructed in the paper by Ren et al. We show that codes formed as the sum of Clifford Unitary Weight Designs (CUWDs) or Coordinate Interleaved Orthogonal Designs (CIODs) exhibit block orthogonal structure. We also provide new construction of block orthogonal codes from Cyclic Division Algebras (CDAs) and Crossed-Product Algebras (CPAs). In addition, we show how the block orthogonal property of the STBCs can be exploited to reduce the decoding complexity of a sphere decoder using a depth first search approach. Simulation results of the decoding complexity show a 30% reduction in the number of floating point operations (FLOPS) of BOSTBCs as compared to STBCs without the block orthogonal structure.

Minimizing the Complexity of Fast Sphere Decoding of STBCs

Decoding of linear space-time block codes (STBCs) with sphere-decoding (SD) is well known. A fast-version of the SD known as fast sphere decoding (FSD) was introduced by Biglieri, Hong and Viterbo. Viewing a linear STBC as a vector space spanned by its defining weight matrices over the real number field, we define a quadratic form (QF), called the Hurwitz-Radon QF (HRQF), on this vector space and give a QF interpretation of the FSD complexity of a linear STBC. It is shown that the FSD complexity is only a function of the weight matrices defining the code and their ordering, and not of the channel realization (even though the equivalent channel when SD is used depends on the channel realization) or the number of receive antennas. It is also shown that the FSD complexity is completely captured into a single matrix obtained from the HRQF. Moreover, for a given set of weight matrices, an algorithm to obtain an optimal ordering of them leading to the least FSD complexity is presented. The well known classes of low FSD complexity codes (multi-group decodable codes, fast decodable codes and fast group decodable codes) are presented in the framework of HRQF.