Physical Layer Network Coding for the K-User Multiple Access Relay Channel

We propose a Physical layer Network Coding (PNC) scheme for the K-user wireless Multiple Access Relay Channel, in which K source nodes want to transmit messages to a destination node D with the help of a relay node R. The proposed scheme involves (i) Phase 1 during which the source nodes alone transmit and (ii) Phase 2 during which the source nodes and the relay node transmit. At the end of Phase 1, the relay node decodes the messages of the source nodes and during Phase 2 transmits a many-to-one function of the decoded messages. To counter the error propagation from the relay node, we propose a novel decoder which takes into account the possibility of error events at R. It is shown that if certain parameters are chosen properly and if the network coding map used at R forms a Latin Hypercube, the proposed decoder offers the maximum diversity order of two. Also, it is shown that for a proper choice of the parameters, the proposed decoder admits fast decoding, with the same decoding complexity order as that of the reference scheme based on Complex Field Network Coding (CFNC). Simulation results indicate that the proposed PNC scheme offers a large gain over the CFNC scheme.

Wireless Network Coding for MIMO Two-Way Relaying

The design of modulation schemes for the physical layer network-coded two-way MIMO relaying scenario is considered, with the denoise-and-forward protocol which employs two phases: Multiple Access phase and Broadcast phase. It is shown that for MIMO two-way relaying, the minimum distance of the effective constellation at the relay becomes zero when all the rows of the channel fade coefficient matrix belong to a finite number of vector subspaces referred to as the singular fade subspaces. The singular fade subspaces can be classified into two kinds based on whether their harmful effects can be removed or not: (i) the removable and (ii) the non-removable singular fade subspaces. It is shown that network coding maps obtained by the completion of appropriate partially filled Latin Rectangles can remove the harmful effects of all the removable singular fade subspaces. For 2(lambda)-PSK signal set, the removable and non-removable singular fade subspaces are characterized and, it is shown that the number of non-removable singular fade subspaces is a small fraction of the total number of singular fade subspaces and this fraction tends to zero as the constellation size tends to infinity. The Latin Rectangles for the case when the end nodes use different number of antennas are shown to be obtainable from the Latin Squares for the case when they use the same number of antennas. Also, the network coding maps which remove all the removable singular singular fade subspaces are shown to be obtainable from a small set of Latin Squares. The removal of all the singular fade subspaces by properly choosing the network coding map, provides a gain of 5.5 dB over the conventional Exclusive-OR network coding, in a Rayleigh fading scenario with 2 antennas at the end nodes and one antenna at the relay node, for 4-PSK signal set.

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.

Spectrum sensing via universal source coding

We consider nonparametric sequential hypothesis testing when the distribution under null hypothesis is fully known and the alternate hypothesis corresponds to some other unknown distribution. We use easily implementable universal lossless source codes to propose simple algorithms for such a setup. These algorithms are motivated from spectrum sensing application in Cognitive Radios. Universal sequential hypothesis testing using Lempel Ziv codes and Krichevsky-Trofimov estimator with Arithmetic Encoder are considered and compared for different distributions. Cooperative spectrum sensing with multiple Cognitive Radios using universal codes is also considered.

Performance analysis of adaptive physical layer network coding for wireless two-way Relaying

The analysis of modulation schemes for the physical layer network-coded two way relaying scenario is presented which employs two phases: Multiple access (MA) phase and Broadcast (BC) phase. Depending on the signal set used at the end nodes, the minimum distance of the effective constellation seen at the relay becomes zero for a finite number of channel fade states referred as the singular fade states. The singular fade states fall into the following two classes: (i) the ones which are caused due to channel outage and whose harmful effect cannot be mitigated by adaptive network coding called the non-removable singular fade states and (ii) the ones which occur due to the choice of the signal set and whose harmful effects can be removed called the removable singular fade states. In this paper, we derive an upper bound on the average end-to-end Symbol Error Rate (SER), with and without adaptive network coding at the relay, for a Rician fading scenario. It is shown that without adaptive network coding, at high Signal to Noise Ratio (SNR), the contribution to the end-to-end SER comes from the following error events which fall as SNR-1: the error events associated with the removable and nonremovable singular fade states and the error event during the BC phase. In contrast, for the adaptive network coding scheme, the error events associated with the removable singular fade states fall as SNR-2, thereby providing a coding gain over the case when adaptive network coding is not used. Also, it is shown that for a Rician fading channel, the error during the MA phase dominates over the error during the BC phase. Hence, adaptive network coding, which improves the performance during the MA phase provides more gain in a Rician fading scenario than in a Rayleigh fading scenario. Furthermore, it is shown that for large Rician factors, among those removable singular fade states which have the same magnitude, those which have the least absolute value of the phase - ngle alone contribute dominantly to the end-to-end SER and it is sufficient to remove the effect of only such singular fade states.

A transform approach to linear network coding for acyclic networks with delay

The algebraic formulation for linear network coding in acyclic networks with each link having an integer delay is well known. Based on this formulation, for a given set of connections over an arbitrary acyclic network with integer delay assumed for the links, the output symbols at the sink nodes at any given time instant is a Fq-linear combination of the input symbols across different generations, where Fq denotes the field over which the network operates. We use finite-field discrete Fourier transform (DFT) to convert the output symbols at the sink nodes at any given time instant into a Fq-linear combination of the input symbols generated during the same generation. We call this as transforming the acyclic network with delay into n-instantaneous networks (n is sufficiently large). We show that under certain conditions, there exists a network code satisfying sink demands in the usual (non-transform) approach if and only if there exists a network code satisfying sink demands in the transform approach. Furthermore, assuming time invariant local encoding kernels, we show that the transform method can be employed to achieve half the rate corresponding to the individual source-destination mincut (which are assumed to be equal to 1) for some classes of three-source three-destination multiple unicast network with delays using alignment strategies when the zero-interference condition is not satisfied.

Fast-Decodable MIDO Codes With Large Coding Gain

In this paper, a new method is proposed to obtain full-diversity, rate-2 (rate of two complex symbols per channel use) space-time block codes (STBCs) that are full-rate for multiple input double output (MIDO) systems. Using this method, rate-2 STBCs for 4 x 2, 6 x 2, 8 x 2, and 12 x 2 systems are constructed and these STBCs are fast ML-decodable, have large coding gains, and STBC-schemes consisting of these STBCs have a non-vanishing determinant (NVD) so that they are DMT-optimal for their respective MIDO systems. It is also shown that the Srinath-Rajan code for the 4 x 2 system, which has the lowest ML-decoding complexity among known rate-2 STBCs for the 4x2 MIDO system with a large coding gain for 4-/16-QAM, has the same algebraic structure as the STBC constructed in this paper for the 4 x 2 system. This also settles in positive a previous conjecture that the STBC-scheme that is based on the Srinath-Rajan code has the NVD property and hence is DMT-optimal for the 4 x 2 system.

Balanced Excitatory and Inhibitory Synaptic Currents Promote Efficient Coding and Metabolic Efficiency

A balance between excitatory and inhibitory synaptic currents is thought to be important for several aspects of information processing in cortical neurons in vivo, including gain control, bandwidth and receptive field structure. These factors will affect the firing rate of cortical neurons and their reliability, with consequences for their information coding and energy consumption. Yet how balanced synaptic currents contribute to the coding efficiency and energy efficiency of cortical neurons remains unclear. We used single compartment computational models with stochastic voltage-gated ion channels to determine whether synaptic regimes that produce balanced excitatory and inhibitory currents have specific advantages over other input regimes. Specifically, we compared models with only excitatory synaptic inputs to those with equal excitatory and inhibitory conductances, and stronger inhibitory than excitatory conductances (i.e. approximately balanced synaptic currents). Using these models, we show that balanced synaptic currents evoke fewer spikes per second than excitatory inputs alone or equal excitatory and inhibitory conductances. However, spikes evoked by balanced synaptic inputs are more informative (bits/spike), so that spike trains evoked by all three regimes have similar information rates (bits/s). Consequently, because spikes dominate the energy consumption of our computational models, approximately balanced synaptic currents are also more energy efficient than other synaptic regimes. Thus, by producing fewer, more informative spikes approximately balanced synaptic currents in cortical neurons can promote both coding efficiency and energy efficiency.

A Communication-Theoretic Framework for 2-DMR Channel Modeling: Performance Evaluation of Coding and Signal Processing Methods

We develop a communication theoretic framework for modeling 2-D magnetic recording channels. Using the model, we define the signal-to-noise ratio (SNR) for the channel considering several physical parameters, such as the channel bit density, code rate, bit aspect ratio, and noise parameters. We analyze the problem of optimizing the bit aspect ratio for maximizing SNR. The read channel architecture comprises a novel 2-D joint self-iterating equalizer and detection system with noise prediction capability. We evaluate the system performance based on our channel model through simulations. The coded performance with the 2-D equalizer detector indicates similar to 5.5 dB of SNR gain over uncoded data.

Consequences of Converting Graded to Action Potentials upon Neural Information Coding and Energy Efficiency

Information is encoded in neural circuits using both graded and action potentials, converting between them within single neurons and successive processing layers. This conversion is accompanied by information loss and a drop in energy efficiency. We investigate the biophysical causes of this loss of information and efficiency by comparing spiking neuron models, containing stochastic voltage-gated Na+ and K+ channels, with generator potential and graded potential models lacking voltage-gated Na+ channels. We identify three causes of information loss in the generator potential that are the by-product of action potential generation: (1) the voltage-gated Na+ channels necessary for action potential generation increase intrinsic noise and (2) introduce non-linearities, and (3) the finite duration of the action potential creates a `footprint' in the generator potential that obscures incoming signals. These three processes reduce information rates by similar to 50% in generator potentials, to similar to 3 times that of spike trains. Both generator potentials and graded potentials consume almost an order of magnitude less energy per second than spike trains. Because of the lower information rates of generator potentials they are substantially less energy efficient than graded potentials. However, both are an order of magnitude more efficient than spike trains due to the higher energy costs and low information content of spikes, emphasizing that there is a two-fold cost of converting analogue to digital; information loss and cost inflation.

Skip Decision and Reference Frame Selection for Low-Complexity H.264/AVC Surveillance Video Coding

H. 264/advanced video coding surveillance video encoders use the Skip mode specified by the standard to reduce bandwidth. They also use multiple frames as reference for motion-compensated prediction. In this paper, we propose two techniques to reduce the bandwidth and computational cost of static camera surveillance video encoders without affecting detection and recognition performance. A spatial sampler is proposed to sample pixels that are segmented using a Gaussian mixture model. Modified weight updates are derived for the parameters of the mixture model to reduce floating point computations. A storage pattern of the parameters in memory is also modified to improve cache performance. Skip selection is performed using the segmentation results of the sampled pixels. The second contribution is a low computational cost algorithm to choose the reference frames. The proposed reference frame selection algorithm reduces the cost of coding uncovered background regions. We also study the number of reference frames required to achieve good coding efficiency. Distortion over foreground pixels is measured to quantify the performance of the proposed techniques. Experimental results show bit rate savings of up to 94.5% over methods proposed in literature on video surveillance data sets. The proposed techniques also provide up to 74.5% reduction in compression complexity without increasing the distortion over the foreground regions in the video sequence.

Linear Index Coding and Representable Discrete Polymatroids

Discrete polymatroids are the multi-set analogue of matroids. In this paper, we explore the connections between linear index coding and representable discrete polymatroids. The index coding problem involves a sender which generates a set of messages X = {x(1), x(2), ... x(k)} and a set of receivers R which demand messages. A receiver R is an element of R is specified by the tuple (x, H) where x. X is the message demanded by R and H subset of X \textbackslash {x} is the side information possessed by R. It is first shown that a linear solution to an index coding problem exists if and only if there exists a representable discrete polymatroid satisfying certain conditions which are determined by the index coding problem considered. El Rouayheb et. al. showed that the problem of finding a multi-linear representation for a matroid can be reduced to finding a perfect linear index coding solution for an index coding problem obtained from that matroid. Multi-linear representation of a matroid can be viewed as a special case of representation of an appropriate discrete polymatroid. We generalize the result of El Rouayheb et. al. by showing that the problem of finding a representation for a discrete polymatroid can be reduced to finding a perfect linear index coding solution for an index coding problem obtained from that discrete polymatroid.

Space-Time Coded Spatial Modulated Physical Layer Network Coding for Two-Way Relaying

Using the spatial modulation approach, where only one transmit antenna is active at a time, we propose two transmission schemes for two-way relay channel using physical layer network coding with space time coding using coordinate interleaved orthogonal designs (CIODs). It is shown that using two uncorrelated transmit antennas at the nodes, but using only one RF transmit chain and space-time coding across these antennas can give a better performance without using any extra resources and without increasing the hardware implementation cost and complexity. In the first transmission scheme, two antennas are used only at the relay, adaptive network coding (ANC) is employed at the relay and the relay transmits a CIOD space time block code (STBC). This gives a better performance compared to an existing ANC scheme for two-way relay channel which uses one antenna each at all the three nodes. It is shown that for this scheme at high SNR the average end-to-end symbol error probability (SEP) is upper bounded by twice the SEP of a point-to-point fading channel. In the second transmission scheme, two transmit antennas are used at all the three nodes, CIOD STBCs are transmitted in multiple access and broadcast phases. This scheme provides a diversity order of two for the average end-to-end SEP with an increased decoding complexity of O(M-3) for an arbitrary signal set and O(M-2 root M) for square QAM signal set. Simulation results show that the proposed schemes performs better than the existing ANC schemes under perfect and imperfect channel state information.

Sparse coding based VLAD for efficient image retrieval

Representing images and videos in the form of compact codes has emerged as an important research interest in the vision community, in the context of web scale image/video search. Recently proposed Vector of Locally Aggregated Descriptors (VLAD), has been shown to outperform the existing retrieval techniques, while giving a desired compact representation. VLAD aggregates the local features of an image in the feature space. In this paper, we propose to represent the local features extracted from an image, as sparse codes over an over-complete dictionary, which is obtained by K-SVD based dictionary training algorithm. The proposed VLAD aggregates the residuals in the space of these sparse codes, to obtain a compact representation for the image. Experiments are performed over the `Holidays' database using SIFT features. The performance of the proposed method is compared with the original VLAD. The 4% increment in the mean average precision (mAP) indicates the better retrieval performance of the proposed sparse coding based VLAD.

Coding of relative size in monkey inferotemporal cortex

We seldom mistake a closer object as being larger, even though its retinal image is bigger. One underlying mechanism could be to calculate the size of the retinal image relative to that of another nearby object. Here we set out to investigate whether single neurons in the monkey inferotemporal cortex (IT) are sensitive to the relative size of parts in a display. Each neuron was tested on shapes containing two parts that could be conjoined or spatially separated. Each shape was presented in four versions created by combining the two parts at each of two possible sizes. In this design, neurons sensitive to the absolute size of parts would show the greatest response modulation when both parts are scaled up, whereas neurons encoding relative size would show similar responses. Our main findings are that 1) IT neurons responded similarly to all four versions of a shape, but tuning tended to be more consistent between versions with proportionately scaled parts; 2) in a subpopulation of cells, we observed interactions that resulted in similar responses to proportionately scaled parts; 3) these interactions developed together with sensitivity to absolute size for objects with conjoined parts but developed slightly later for objects with spatially separate parts. Taken together, our results demonstrate for the first time that there is a subpopulation of neurons in IT that encodes the relative size of parts in a display, forming a potential neural substrate for size constancy.