Wireless Network-Coded Bidirectional Relaying Using Latin Squares for M-PSK Modulation

The design of modulation schemes for the physical layer network-coded two-way relaying scenario is considered with a protocol which employs two phases: multiple access (MA) phase and broadcast (BC) phase. It was observed by Koike-Akino et al. that adaptively changing the network coding map used at the relay according to the channel conditions greatly reduces the impact of MA interference which occurs at the relay during the MA phase and all these network coding maps should satisfy a requirement called the exclusive law. We show that every network coding map that satisfies the exclusive law is representable by a Latin Square and conversely, that this relationship can be used to get the network coding maps satisfying the exclusive law. The channel fade states for which the minimum distance of the effective constellation at the relay become zero are referred to as the singular fade states. For M - PSK modulation (M any power of 2), it is shown that there are (M-2/4 - M/2 + 1) M singular fade states. Also, it is shown that the constraints which the network coding maps should satisfy so that the harmful effects of the singular fade states are removed, can be viewed equivalently as partially filled Latin Squares (PFLS). The problem of finding all the required maps is reduced to finding a small set of maps for M - PSK constellations (any power of 2), obtained by the completion of PFLS. Even though the completability of M x M PFLS using M symbols is an open problem, specific cases where such a completion is always possible are identified and explicit construction procedures are provided. Having obtained the network coding maps, the set of all possible channel realizations (the complex plane) is quantized into a finite number of regions, with a specific network coding map chosen in a particular region. It is shown that the complex plane can be partitioned into two regions: a region in which any network coding map which satisfies the exclusive law gives the same best performance and a region in which the choice of the network coding map affects the performance. The quantization thus obtained analytically, leads to the same as the one obtained using computer search for M = 4-PSK signal set by Koike-Akino et al., when specialized for Simulation results show that the proposed scheme performs better than the conventional exclusive-OR (XOR) network coding and in some cases outperforms the scheme proposed by Koike-Akino et al.

Physical layer network coding for two-way relaying with QAM and latin squares

In the design of modulation schemes for the physical layer network-coded two way relaying scenario with two phases (Multiple access (MA) Phase and Broadcast (BC) Phase), it was observed by Koike-Akino et al. that adaptively changing the network coding map used at the relay according to the channel conditions greatly reduces the impact of multiple access interference and all these network coding maps should satisfy a requirement called the exclusive law. In [11] the case in which the end nodes use M-PSK signal sets is extensively studied using Latin Squares. This paper deals with the case in which the end nodes use square M-QAM signal sets. In a fading scenario, for certain channel conditions, termed singular fade states, the MA phase performance is greatly reduced. We show that the square QAM signal sets lead to lesser number of singular fade states compared to PSK signal sets. Because of this, the complexity at the relay is enormously reduced. Moreover lesser number of overhead bits are required in the BC phase. We find the number of singular fade states for PAM and QAM signal sets used at the end nodes. The fade state γejθ = 1 is a singular fade state for M-QAM for all values of M and it is shown that certain block circulant Latin Squares remove this singular fade state. Simulation results are presented to show that QAM signal set perform better than PSK.

Wireless network-coded three-way relaying using Latin Cubes

The design of modulation schemes for the physical layer network-coded three-way wireless relaying scenario is considered. The protocol employs two phases: Multiple Access (MA) phase and Broadcast (BC) phase with each phase utilizing one channel use. For the two-way relaying scenario, it was observed by Koike-Akino et al. [4], that adaptively changing the network coding map used at the relay according to the channel conditions greatly reduces the impact of multiple access interference which occurs at the relay during the MA phase and all these network coding maps should satisfy a requirement called exclusive law. This paper does the equivalent for the three-way relaying scenario. We show that when the three users transmit points from the same 4-PSK constellation, every such network coding map that satisfies the exclusive law can be represented by a Latin Cube of Second Order. The network code map used by the relay for the BC phase is explicitly obtained and is aimed at reducing the effect of interference at the MA stage.

Wireless bidirectional relaying and Latin squares

The design of modulation schemes for the physical layer network-coded two way relaying scenario is considered with the protocol which employs two phases: Multiple access (MA) Phase and Broadcast (BC) Phase. It was observed by Koike-Akino et al. that adaptively changing the network coding map used at the relay according to the channel conditions greatly reduces the impact of multiple access interference which occurs at the relay during the MA Phase and all these network coding maps should satisfy a requirement called the exclusive law. We show that every network coding map that satisfies the exclusive law is representable by a Latin Square and conversely, and this relationship can be used to get the network coding maps satisfying the exclusive law. Using the structural properties of the Latin Squares for a given set of parameters, the problem of finding all the required maps is reduced to finding a small set of maps for M-PSK constellations. This is achieved using the notions of isotopic and transposed Latin Squares. Furthermore, the channel conditions for which the bit-wise XOR will perform well is analytically obtained which holds for all values of M (for M any power of 2). We illustrate these results for the case where both the end users use QPSK constellation.

PolyGLoT: A Polyhedral Loop Transformation Framework for a Graphical Dataflow Language

Polyhedral techniques for program transformation are now used in several proprietary and open source compilers. However, most of the research on polyhedral compilation has focused on imperative languages such as C, where the computation is specified in terms of statements with zero or more nested loops and other control structures around them. Graphical dataflow languages, where there is no notion of statements or a schedule specifying their relative execution order, have so far not been studied using a powerful transformation or optimization approach. The execution semantics and referential transparency of dataflow languages impose a different set of challenges. In this paper, we attempt to bridge this gap by presenting techniques that can be used to extract polyhedral representation from dataflow programs and to synthesize them from their equivalent polyhedral representation. We then describe PolyGLoT, a framework for automatic transformation of dataflow programs which we built using our techniques and other popular research tools such as Clan and Pluto. For the purpose of experimental evaluation, we used our tools to compile LabVIEW, one of the most widely used dataflow programming languages. Results show that dataflow programs transformed using our framework are able to outperform those compiled otherwise by up to a factor of seventeen, with a mean speed-up of 2.30x while running on an 8-core Intel system.

Influence of Spatial Variability on Pavement Responses Using Latin Hypercube Sampling on Two-Dimensional Random Fields

Although uncertainties in material properties have been addressed in the design of flexible pavements, most current modeling techniques assume that pavement layers are homogeneous. The paper addresses the influence of the spatial variability of the resilient moduli of pavement layers by evaluating the effect of the variance and correlation length on the pavement responses to loading. The integration of the spatially varying log-normal random field with the finite-difference method has been achieved through an exponential autocorrelation function. The variation in the correlation length was found to have a marginal effect on the mean values of the critical strains and a noticeable effect on the standard deviation which decreases with decreases in correlation length. This reduction in the variance arises because of the spatial averaging phenomenon over the softer and stiffer zones generated because of spatial variability. The increase in the mean value of critical strains with decreasing correlation length, although minor, illustrates that pavement performance is adversely affected by the presence of spatially varying layers. The study also confirmed that the higher the variability in the pavement layer moduli, introduced through a higher value of coefficient of variation (COV), the higher the variability in the pavement response. The study concludes that ignoring spatial variability by modeling the pavement layers as homogeneous that have very short correlation lengths can result in the underestimation of the critical strains and thus an inaccurate assessment of the pavement performance. (C) 2014 American Society of Civil Engineers.

Translation Induction on Indian Language Corpora Using Translingual Themes from Other Languages

Identifying translations from comparable corpora is a well-known problem with several applications, e.g. dictionary creation in resource-scarce languages. Scarcity of high quality corpora, especially in Indian languages, makes this problem hard, e.g. state-of-the-art techniques achieve a mean reciprocal rank (MRR) of 0.66 for English-Italian, and a mere 0.187 for Telugu-Kannada. There exist comparable corpora in many Indian languages with other ``auxiliary'' languages. We observe that translations have many topically related words in common in the auxiliary language. To model this, we define the notion of a translingual theme, a set of topically related words from auxiliary language corpora, and present a probabilistic framework for translation induction. Extensive experiments on 35 comparable corpora using English and French as auxiliary languages show that this approach can yield dramatic improvements in performance (e.g. MRR improves by 124% to 0.419 for Telugu-Kannada). A user study on WikiTSu, a system for cross-lingual Wikipedia title suggestion that uses our approach, shows a 20% improvement in the quality of titles suggested.

Falcon: A Graph Manipulation Language for Heterogeneous Systems

Graph algorithms have been shown to possess enough parallelism to keep several computing resources busy-even hundreds of cores on a GPU. Unfortunately, tuning their implementation for efficient execution on a particular hardware configuration of heterogeneous systems consisting of multicore CPUs and GPUs is challenging, time consuming, and error prone. To address these issues, we propose a domain-specific language (DSL), Falcon, for implementing graph algorithms that (i) abstracts the hardware, (ii) provides constructs to write explicitly parallel programs at a higher level, and (iii) can work with general algorithms that may change the graph structure (morph algorithms). We illustrate the usage of our DSL to implement local computation algorithms (that do not change the graph structure) and morph algorithms such as Delaunay mesh refinement, survey propagation, and dynamic SSSP on GPU and multicore CPUs. Using a set of benchmark graphs, we illustrate that the generated code performs close to the state-of-the-art hand-tuned implementations.

Error Correcting Functional Source Coding with Decoder Side Information using Row-Latin Rectangles

The functional source coding problem in which the receiver side information (Has-set) and demands (Want-set) include functions of source messages is studied using row-Latin rectangle. The source transmits encoded messages, called the functional source code, in order to satisfy the receiver's demands. We obtain a minimum length using the row-Latin rectangle. Next, we consider the case of transmission errors and provide a necessary and sufficient condition that a functional source code must satisfy so that the receiver can correctly decode the values of the functions in its Want-set.