A digital interface for Gaussian relay networks: lifting codes from the discrete superposition model to Gaussian relay networks

For every Gaussian relay network with a single source-destination pair, it is known that there exists a corresponding deterministic network called the discrete superposition network that approximates its capacity uniformly over all SNR's to within a bounded number of bits. The next step in this program of rigorous approximation is to determine whether coding schemes for discrete superposition models can be lifted to Gaussian relay networks with a bounded rate loss independent of SNR. We establish precisely this property and show that the superposition model can thus serve as a strong surrogate for designing codes for Gaussian relay networks. We show that a code for a Gaussian relay network, with a single source-destination pair and multiple relay nodes, can be designed from any code for the corresponding discrete superposition network simply by pruning it. In comparison to the rate of the discrete superposition network's code, the rate of the Gaussian network's code only reduces at most by a constant that is a function only of the number of nodes in the network and independent of channel gains. This result is also applicable for coding schemes for MIMO Gaussian relay networks, with the reduction depending additionally on the number of antennas. Hence, the discrete superposition model can serve as a digital interface for operating Gaussian relay networks.Comment: 5 pages, 2010 IEEE Information Theory Workshop, Cair

A digital interface for Gaussian relay and interference networks: Lifting codes from the discrete superposition model

For every Gaussian network, there exists a corresponding deterministic network called the discrete superposition network. We show that this discrete superposition network provides a near-optimal digital interface for operating a class consisting of many Gaussian networks in the sense that any code for the discrete superposition network can be naturally lifted to a corresponding code for the Gaussian network, while achieving a rate that is no more than a constant number of bits lesser than the rate it achieves for the discrete superposition network. This constant depends only on the number of nodes in the network and not on the channel gains or SNR. Moreover the capacities of the two networks are within a constant of each other, again independent of channel gains and SNR. We show that the class of Gaussian networks for which this interface property holds includes relay networks with a single source-destination pair, interference networks, multicast networks, and the counterparts of these networks with multiple transmit and receive antennas. The code for the Gaussian relay network can be obtained from any code for the discrete superposition network simply by pruning it. This lifting scheme establishes that the superposition model can indeed potentially serve as a strong surrogate for designing codes for Gaussian relay networks. We present similar results for the K x K Gaussian interference network, MIMO Gaussian interference networks, MIMO Gaussian relay networks, and multicast networks, with the constant gap depending additionally on the number of antennas in case of MIMO networks.Comment: Final versio

Low Correlation Sequences over the QAM Constellation

This paper presents the first concerted look at low correlation sequence families over QAM constellations of size M^2=4^m and their potential applicability as spreading sequences in a CDMA setting. Five constructions are presented, and it is shown how such sequence families have the ability to transport a larger amount of data as well as enable variable-rate signalling on the reverse link. Canonical family CQ has period N, normalized maximum-correlation parameter theta_max bounded above by A sqrt(N), where 'A' ranges from 1.8 in the 16-QAM case to 3.0 for large M. In a CDMA setting, each user is enabled to transfer 2m bits of data per period of the spreading sequence which can be increased to 3m bits of data by halving the size of the sequence family. The technique used to construct CQ is easily extended to produce larger sequence families and an example is provided. Selected family SQ has a lower value of theta_max but permits only (m+1)-bit data modulation. The interleaved 16-QAM sequence family IQ has theta_max <= sqrt(2) sqrt(N) and supports 3-bit data modulation. The remaining two families are over a quadrature-PAM (Q-PAM) subset of size 2M of the M^2-QAM constellation. Family P has a lower value of theta_max in comparison with Family SQ, while still permitting (m+1)-bit data modulation. Interleaved family IP, over the 8-ary Q-PAM constellation, permits 3-bit data modulation and interestingly, achieves the Welch lower bound on theta_max.Comment: 21 pages, 3 figures. To appear in IEEE Transactions on Information Theory in February 200

Supersensitive measurement of angular displacements using entangled photons

We show that the use of entangled photons having non-zero orbital angular momentum (OAM) increases the resolution and sensitivity of angular-displacement measurements performed using an interferometer. By employing a 4$\times$4 matrix formulation to study the propagation of entangled OAM modes, we analyze measurement schemes for two and four entangled photons and obtain explicit expressions for the resolution and sensitivity in these schemes. We find that the resolution of angular-displacement measurements scales as $Nl$ while the angular sensitivity increases as $1/(2Nl)$, where $N$ is the number of entangled photons and $l$ the magnitude of the orbital-angular-momentum mode index. These results are an improvement over what could be obtained with $N$ non-entangled photons carrying an orbital angular momentum of $l\hbar$ per photonComment: 6 pages, 3 figure

PHOSPHATE SOLUBILIZING MICROBES: AN EFFECTIVE AND ALTERNATIVE APPROACH AS BIOFERTILIZERS

It is undoubtedly clear that phosphorus is the second most important nutrient after nitrogen required for growth of plants. It is an essential element in all living systems. Hardly 1%-2% of phosphorous is supplied to other parts of the plants. Plants acquire phosphorus from soil solution in the form of phosphate anion. It is the least mobile element in plant and soil in comparison to other macronutrients. It remains in a precipitated form in the soil as mono or orthophosphate or is absorbed by Fe or Al oxides through legend exchange. Generally, the phosphate solubilizing microorganisms (PSM) play a very important role in phosphorus nutrition by exchanging its availability to plants through release from inorganic and organic soil phosphorus pools by solubilization and mineralization. The main mechanism in the soil for mineral phosphate solubilization is by lowering the soil pH by the microbial production of organic acids and mineralization of organic phosphorus by acid phosphates. To fulfill the phosphorous demand of plant, an additional source of phosphorous is applied to plants in the form of chemical fertilizers. One of the most common forms of phosphate is fertilizers in the form of rock phosphate or superphosphate. It is not suggested to apply these phosphates directly to soil as there are so many environmental problems. Hence, biofertilizers or microbial inoculants are used as an alternate source, which are both economic as well as eco-friendly.Â