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Register a new userPreserving Confidentiality in The Gaussian Broadcast Channel Using Compute-and-Forward
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Added by
Parisa Babaheidarian
Publication date
2017
fields
Informatics Engineering
and research's language is
English
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We study the transmission of confidential messages across a wireless broadcast channel with K>2 receivers and K helpers. The goal is to transmit all messages reliably to their intended receivers while keeping them confidential from the unintended receivers. We design a codebook based on nested lattice structure, cooperative jamming, lattice alignment, and i.i.d. coding. Moreover, we exploit the asymmetric compute-and-forward decoding strategy to handle finite SNR regimes. Unlike previous alignment schemes, our achievable rates are attainable at any finite SNR value. Also, we show that our scheme achieves the optimal sum secure degrees of freedom of 1 for the K-receiver Gaussian broadcast channel with K confidential messages and K helpers.
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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.
Integer-forcing (IF) precoding, also known as downlink IF, is a promising new approach for communication over multiple-input multiple-output (MIMO) broadcast channels. Inspired by the integer-forcing linear receiver for multiple-access channels, it generalizes linear precoding by inducing an effective channel matrix that is approximately integer, rather than approximately identity. Combined with lattice encoding and a pre-inversion of the channel matrix at the transmitter, the scheme has the potential to outperform any linear precoding scheme, despite enjoying similar low complexity. In this paper, a specific IF precoding scheme, called diagonally-scaled exact IF (DIF), is proposed and shown to achieve maximum spatial multiplexing gain. For the special case of two receivers, in the high SNR regime, an optimal choice of parameters is derived analytically, leading to an almost closed-form expression for the achievable sum rate. In particular, it is shown that the gap to the sum capacity is upper bounded by 0.27 bits for any channel realization. For general SNR, a regularized version of DIF (RDIF) is proposed. Numerical results for two receivers under Rayleigh fading show that RDIF can achieve performance superior to optimal linear precoding and very close to the sum capacity.
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.
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.
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