14 research outputs found
Decoding by Embedding: Correct Decoding Radius and DMT Optimality
The closest vector problem (CVP) and shortest (nonzero) vector problem (SVP)
are the core algorithmic problems on Euclidean lattices. They are central to
the applications of lattices in many problems of communications and
cryptography. Kannan's \emph{embedding technique} is a powerful technique for
solving the approximate CVP, yet its remarkable practical performance is not
well understood. In this paper, the embedding technique is analyzed from a
\emph{bounded distance decoding} (BDD) viewpoint. We present two complementary
analyses of the embedding technique: We establish a reduction from BDD to
Hermite SVP (via unique SVP), which can be used along with any Hermite SVP
solver (including, among others, the Lenstra, Lenstra and Lov\'asz (LLL)
algorithm), and show that, in the special case of LLL, it performs at least as
well as Babai's nearest plane algorithm (LLL-aided SIC). The former analysis
helps to explain the folklore practical observation that unique SVP is easier
than standard approximate SVP. It is proven that when the LLL algorithm is
employed, the embedding technique can solve the CVP provided that the noise
norm is smaller than a decoding radius , where
is the minimum distance of the lattice, and . This
substantially improves the previously best known correct decoding bound . Focusing on the applications of BDD to decoding of
multiple-input multiple-output (MIMO) systems, we also prove that BDD of the
regularized lattice is optimal in terms of the diversity-multiplexing gain
tradeoff (DMT), and propose practical variants of embedding decoding which
require no knowledge of the minimum distance of the lattice and/or further
improve the error performance.Comment: To appear in IEEE Transactions on Information Theor
Precoded Integer-Forcing Universally Achieves the MIMO Capacity to Within a Constant Gap
An open-loop single-user multiple-input multiple-output communication scheme
is considered where a transmitter, equipped with multiple antennas, encodes the
data into independent streams all taken from the same linear code. The coded
streams are then linearly precoded using the encoding matrix of a perfect
linear dispersion space-time code. At the receiver side, integer-forcing
equalization is applied, followed by standard single-stream decoding. It is
shown that this communication architecture achieves the capacity of any
Gaussian multiple-input multiple-output channel up to a gap that depends only
on the number of transmit antennas.Comment: to appear in the IEEE Transactions on Information Theor
Distributed space-time coding including the golden code with application in cooperative networks
This thesis presents new methodologies to improve performance of wireless cooperative networks using the Golden Code. As a form of space-time coding, the Golden Code can achieve diversity-multiplexing tradeoff and the data rate can be twice that of the Alamouti code. In practice, however, asynchronism between relay nodes may reduce performance and channel quality can be degraded from certain antennas.
Firstly, a simple offset transmission scheme, which employs full interference cancellation (FIC) and orthogonal frequency division multiplexing (OFDM), is enhanced through the use of four relay nodes and receiver processing to mitigate asynchronism. Then, the potential reduction in diversity gain due to the dependent channel matrix elements in the distributed Golden Code transmission, and the rate penalty of multihop transmission, are mitigated by relay selection based on two-way transmission. The Golden Code is also implemented in an asynchronous one-way relay network over frequency flat and selective channels, and a simple approach to overcome asynchronism is proposed. In one-way communication with computationally efficient sphere decoding, the maximum of the channel parameter means is shown to achieve the best performance for the relay selection through bit error rate simulations.
Secondly, to reduce the cost of hardware when multiple antennas are available in a cooperative network, multi-antenna selection is exploited. In this context, maximum-sum transmit antenna selection is proposed. End-to-end signal-to-noise ratio (SNR) is calculated and outage probability analysis is performed when the links are modelled as Rayleigh fading frequency flat channels. The numerical results support the analysis and for a MIMO system
maximum-sum selection is shown to outperform maximum-minimum selection. Additionally, pairwise error probability (PEP) analysis is performed for maximum-sum transmit antenna selection with the Golden Code and the diversity order is obtained.
Finally, with the assumption of fibre-connected multiple antennas with finite buffers, multiple-antenna selection is implemented on the basis of maximum-sum antenna selection. Frequency flat Rayleigh fading channels are assumed together with a decode and forward transmission scheme. Outage probability analysis is performed by exploiting the steady-state stationarity of a Markov Chain model