14,702 research outputs found
DMT Optimality of LR-Aided Linear Decoders for a General Class of Channels, Lattice Designs, and System Models
The work identifies the first general, explicit, and non-random MIMO
encoder-decoder structures that guarantee optimality with respect to the
diversity-multiplexing tradeoff (DMT), without employing a computationally
expensive maximum-likelihood (ML) receiver. Specifically, the work establishes
the DMT optimality of a class of regularized lattice decoders, and more
importantly the DMT optimality of their lattice-reduction (LR)-aided linear
counterparts. The results hold for all channel statistics, for all channel
dimensions, and most interestingly, irrespective of the particular lattice-code
applied. As a special case, it is established that the LLL-based LR-aided
linear implementation of the MMSE-GDFE lattice decoder facilitates DMT optimal
decoding of any lattice code at a worst-case complexity that grows at most
linearly in the data rate. This represents a fundamental reduction in the
decoding complexity when compared to ML decoding whose complexity is generally
exponential in rate.
The results' generality lends them applicable to a plethora of pertinent
communication scenarios such as quasi-static MIMO, MIMO-OFDM, ISI,
cooperative-relaying, and MIMO-ARQ channels, in all of which the DMT optimality
of the LR-aided linear decoder is guaranteed. The adopted approach yields
insight, and motivates further study, into joint transceiver designs with an
improved SNR gap to ML decoding.Comment: 16 pages, 1 figure (3 subfigures), submitted to the IEEE Transactions
on Information Theor
Achieving a vanishing SNR-gap to exact lattice decoding at a subexponential complexity
The work identifies the first lattice decoding solution that achieves, in the
general outage-limited MIMO setting and in the high-rate and high-SNR limit,
both a vanishing gap to the error-performance of the (DMT optimal) exact
solution of preprocessed lattice decoding, as well as a computational
complexity that is subexponential in the number of codeword bits. The proposed
solution employs lattice reduction (LR)-aided regularized (lattice) sphere
decoding and proper timeout policies. These performance and complexity
guarantees hold for most MIMO scenarios, all reasonable fading statistics, all
channel dimensions and all full-rate lattice codes.
In sharp contrast to the above manageable complexity, the complexity of other
standard preprocessed lattice decoding solutions is shown here to be extremely
high. Specifically the work is first to quantify the complexity of these
lattice (sphere) decoding solutions and to prove the surprising result that the
complexity required to achieve a certain rate-reliability performance, is
exponential in the lattice dimensionality and in the number of codeword bits,
and it in fact matches, in common scenarios, the complexity of ML-based
solutions. Through this sharp contrast, the work was able to, for the first
time, rigorously quantify the pivotal role of lattice reduction as a special
complexity reducing ingredient.
Finally the work analytically refines transceiver DMT analysis which
generally fails to address potentially massive gaps between theory and
practice. Instead the adopted vanishing gap condition guarantees that the
decoder's error curve is arbitrarily close, given a sufficiently high SNR, to
the optimal error curve of exact solutions, which is a much stronger condition
than DMT optimality which only guarantees an error gap that is subpolynomial in
SNR, and can thus be unbounded and generally unacceptable in practical
settings.Comment: 16 pages - submission for IEEE Trans. Inform. Theor
Semantically Secure Lattice Codes for Compound MIMO Channels
We consider compound multi-input multi-output (MIMO) wiretap channels where
minimal channel state information at the transmitter (CSIT) is assumed. Code
construction is given for the special case of isotropic mutual information,
which serves as a conservative strategy for general cases. Using the flatness
factor for MIMO channels, we propose lattice codes universally achieving the
secrecy capacity of compound MIMO wiretap channels up to a constant gap
(measured in nats) that is equal to the number of transmit antennas. The
proposed approach improves upon existing works on secrecy coding for MIMO
wiretap channels from an error probability perspective, and establishes
information theoretic security (in fact semantic security). We also give an
algebraic construction to reduce the code design complexity, as well as the
decoding complexity of the legitimate receiver. Thanks to the algebraic
structures of number fields and division algebras, our code construction for
compound MIMO wiretap channels can be reduced to that for Gaussian wiretap
channels, up to some additional gap to secrecy capacity.Comment: IEEE Trans. Information Theory, to appea
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
Error- and Loss-Tolerances of Surface Codes with General Lattice Structures
We propose a family of surface codes with general lattice structures, where
the error-tolerances against bit and phase errors can be controlled
asymmetrically by changing the underlying lattice geometries. The surface codes
on various lattices are found to be efficient in the sense that their threshold
values universally approach the quantum Gilbert-Varshamov bound. We find that
the error-tolerance of surface codes depends on the connectivity of underlying
lattices; the error chains on a lattice of lower connectivity are easier to
correct. On the other hand, the loss-tolerance of surface codes exhibits an
opposite behavior; the logical information on a lattice of higher connectivity
has more robustness against qubit loss. As a result, we come upon a fundamental
trade-off between error- and loss-tolerances in the family of the surface codes
with different lattice geometries.Comment: 5pages, 3 figure
Cyclic division algebras: a tool for space-time coding
Multiple antennas at both the transmitter and receiver ends of a wireless digital transmission channel may increase both data rate and reliability. Reliable high rate transmission over such channels can only be achieved through Space–Time coding. Rank and determinant code design criteria have been proposed to enhance diversity and coding gain. The special case of full-diversity criterion requires that the difference of any two distinct codewords has full rank.
Extensive work has been done on Space–Time coding, aiming at
finding fully diverse codes with high rate. Division algebras have been proposed as a new tool for constructing Space–Time codes, since they are non-commutative algebras that naturally yield linear fully diverse codes. Their algebraic properties can thus be further exploited to
improve the design of good codes.
The aim of this work is to provide a tutorial introduction to the algebraic tools involved in the design of codes based on cyclic division algebras. The different design criteria involved will be illustrated, including the constellation shaping, the information lossless property, the non-vanishing determinant property, and the diversity multiplexing trade-off. The final target is to give the complete mathematical background underlying the construction of the Golden code and the other Perfect Space–Time block codes
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