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.

Simulating grasping behavior of people using the relational description scheme

This paper presents an enhanced relational description for the prescription of the grasp requirement and evolution of the posture of a digital human hand towards satisfaction of this requirement. Precise relational description needs anatomical segmentation of the hand geometry into palmar, dorsal and lateral patches using the palm-plane and joint locations information, and operational segmentation of the object geometry into pull,push and lateral patches with due consideration to the effect of friction. Relational description identifies appropriate patches for a desired grasp condition. Satisfaction of this requirement occurs in two discrete stages,namely,contact establishment and post-contact force exertion for object capturing. Contact establishment occurs in four potentially overlapping phases,namely,re-orientation,transfer,pre- shaping,and closing-in. The novel h and re-orientation phase,enables the palm to face the object in a task sequence scenario, transfer takes the wrist to the ball park ; pre-shaping and close-in finally achieves the contact. In this paper, an anatomically pertinent closed-form formulation is presented for the closing-in phase for identification of the point of contact on the patches ,prescribed by the relational description. Since mere contact does not ensure grasp and slip phenomenon at the point of contact on application of force is a common occurrence, the effect of slip in presence of friction has been studied for 2D and 3D object grasping endeavours and a computational generation of the slip locus is presented.A general slip locus is found to be a non-linear curve even on planar faces.Two varieties of slip phenomena,namely,stabilizing and non-stabilizing slips, and their local characteristics have been identified.Study of the evolution of this slip characteristic over the slip locus exhibited diverse grasping behaviour possibilities. Thus, the relational description paradigm not only makes the requirement specification easy and meaningful but also enables high fidelity hand object interaction studies possible.

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.

A relational contract for water demand management

For necessary goods like water, under supply constraints, fairness considerations lead to negative externalities. The objective of this paper is to design an infinite horizon contract or relational contract (a type of long-term contract) that ensures self-enforcing (instead of court-enforced) behaviour by the agents to mitigate the externality due to fairness issues. In this contract, the consumer is induced to consume at firm-supply level using the threat of higher fair price for future time periods. The pricing mechanism, computed in this paper, internalizes the externality and is shown to be economically efficient and provides revenue sufficiency.

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.

Dynamic multi-relational Chinese restaurant process for analyzing influences on users in social media

We study the problem of analyzing influence of various factors affecting individual messages posted in social media. The problem is challenging because of various types of influences propagating through the social media network that act simultaneously on any user. Additionally, the topic composition of the influencing factors and the susceptibility of users to these influences evolve over time. This problem has not been studied before, and off-the-shelf models are unsuitable for this purpose. To capture the complex interplay of these various factors, we propose a new non-parametric model called the Dynamic Multi-Relational Chinese Restaurant Process. This accounts for the user network for data generation and also allows the parameters to evolve over time. Designing inference algorithms for this model suited for large scale social-media data is another challenge. To this end, we propose a scalable and multi-threaded inference algorithm based on online Gibbs Sampling. Extensive evaluations on large-scale Twitter and Face book data show that the extracted topics when applied to authorship and commenting prediction outperform state-of-the-art baselines. More importantly, our model produces valuable insights on topic trends and user personality trends beyond the capability of existing approaches.

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.

On t-designs and bounds relating query complexity to error resilience in locally correctable codes

An n-length block code C is said to be r-query locally correctable, if for any codeword x ∈ C, one can probabilistically recover any one of the n coordinates of the codeword x by querying at most r coordinates of a possibly corrupted version of x. It is known that linear codes whose duals contain 2-designs are locally correctable. In this article, we consider linear codes whose duals contain t-designs for larger t. It is shown here that for such codes, for a given number of queries r, under linear decoding, one can, in general, handle a larger number of corrupted bits. We exhibit to our knowledge, for the first time, a finite length code, whose dual contains 4-designs, which can tolerate a fraction of up to 0.567/r corrupted symbols as against a maximum of 0.5/r in prior constructions. We also present an upper bound that shows that 0.567 is the best possible for this code length and query complexity over this symbol alphabet thereby establishing optimality of this code in this respect. A second result in the article is a finite-length bound which relates the number of queries r and the fraction of errors that can be tolerated, for a locally correctable code that employs a randomized algorithm in which each instance of the algorithm involves t-error correction.