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Register a new userCompute-and-Forward: Finding the Best Equation
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Added by
Saeid Sahraei
Publication date
2014
fields
Informatics Engineering
and research's language is
English
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Compute-and-Forward is an emerging technique to deal with interference. It allows the receiver to decode a suitably chosen integer linear combination of the transmitted messages. The integer coefficients should be adapted to the channel fading state. Optimizing these coefficients is a Shortest Lattice Vector (SLV) problem. In general, the SLV problem is known to be prohibitively complex. In this paper, we show that the particular SLV instance resulting from the Compute-and-Forward problem can be solved in low polynomial complexity and give an explicit deterministic algorithm that is guaranteed to find the optimal solution.
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We present a modified compute-and-forward scheme which utilizes Channel State Information at the Transmitters (CSIT) in a natural way. The modified scheme allows different users to have different coding rates, and use CSIT to achieve larger rate region. This idea is applicable to all systems which use the compute-and-forward technique and can be arbitrarily better than the regular scheme in some settings.
The compute-and-forward (CoF) is a relaying protocol, which uses algebraic structured codes to harness the interference and remove the noise in wireless networks. We propose the use of phase precoders at the transmitters of a network, where relays apply CoF strategy. We define the {em phase precoded computation rate} and show that it is greater than the original computation rate of CoF protocol. We further give a new low-complexity method for finding network equations. We finally show that the proposed precoding scheme increases the degrees-of-freedom (DoF) of CoF protocol. This overcomes the limitations on the DoF of the CoF protocol, recently presented by Niesen and Whiting. Using tools from Diophantine approximation and algebraic geometry, we prove the existence of a phase precoder that approaches the maximum DoF when the number of transmitters tends to infinity.
In a recent work, Nazer and Gastpar proposed the Compute-and-Forward strategy as a physical-layer network coding scheme. They described a code structure based on nested lattices whose algebraic structure makes the scheme reliable and efficient. In this work, we consider the implementation of their scheme for real Gaussian channels and one dimensional lattices. We relate the maximization of the transmission rate to the lattice shortest vector problem. We explicit, in this case, the maximum likelihood criterion and show that it can be implemented by using an Inhomogeneous Diophantine Approximation algorithm.
Lattice codes used under the Compute-and-Forward paradigm suggest an alternative strategy for the standard Gaussian multiple-access channel (MAC): The receiver successively decodes integer linear combinations of the messages until it can invert and recover all messages. In this paper, a multiple-access technique called CFMA (Compute-Forward Multiple Access) is proposed and analyzed. For the two-user MAC, it is shown that without time-sharing, the entire capacity region can be attained using CFMA with a single-user decoder as soon as the signal-to-noise ratios are above $1+sqrt{2}$. A partial analysis is given for more than two users. Lastly the strategy is extended to the so-called dirty MAC where two interfering signals are known non-causally to the two transmitters in a distributed fashion. Our scheme extends the previously known results and gives new achievable rate regions.
Interference Alignment is a new solution to over- come the problem of interference in multiuser wireless com- munication systems. Recently, the Compute-and-Forward (CF) transform has been proposed to approximate the capacity of K- user Gaussian Symmetric Interference Channel and practically perform Interference Alignment in wireless networks. However, this technique shows a random behavior in the achievable sum- rate, especially at high SNR. In this work, the origin of this random behavior is analyzed and a novel precoding technique based on the Golden Ratio is proposed to scale down the fadings experiences by the achievable sum-rate at high SNR.
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