41,693 research outputs found
Low Density Lattice Codes
Low density lattice codes (LDLC) are novel lattice codes that can be decoded
efficiently and approach the capacity of the additive white Gaussian noise
(AWGN) channel. In LDLC a codeword x is generated directly at the n-dimensional
Euclidean space as a linear transformation of a corresponding integer message
vector b, i.e., x = Gb, where H, the inverse of G, is restricted to be sparse.
The fact that H is sparse is utilized to develop a linear-time iterative
decoding scheme which attains, as demonstrated by simulations, good error
performance within ~0.5dB from capacity at block length of n = 100,000 symbols.
The paper also discusses convergence results and implementation considerations.Comment: 24 pages, 4 figures. Submitted for publication in IEEE transactions
on Information Theor
Precoding by Pairing Subchannels to Increase MIMO Capacity with Discrete Input Alphabets
We consider Gaussian multiple-input multiple-output (MIMO) channels with
discrete input alphabets. We propose a non-diagonal precoder based on the
X-Codes in \cite{Xcodes_paper} to increase the mutual information. The MIMO
channel is transformed into a set of parallel subchannels using Singular Value
Decomposition (SVD) and X-Codes are then used to pair the subchannels. X-Codes
are fully characterized by the pairings and a real rotation matrix
for each pair (parameterized with a single angle). This precoding structure
enables us to express the total mutual information as a sum of the mutual
information of all the pairs. The problem of finding the optimal precoder with
the above structure, which maximizes the total mutual information, is solved by
{\em i}) optimizing the rotation angle and the power allocation within each
pair and {\em ii}) finding the optimal pairing and power allocation among the
pairs. It is shown that the mutual information achieved with the proposed
pairing scheme is very close to that achieved with the optimal precoder by Cruz
{\em et al.}, and is significantly better than Mercury/waterfilling strategy by
Lozano {\em et al.}. Our approach greatly simplifies both the precoder
optimization and the detection complexity, making it suitable for practical
applications.Comment: submitted to IEEE Transactions on Information Theor
Cyclic-Coded Integer-Forcing Equalization
A discrete-time intersymbol interference channel with additive Gaussian noise
is considered, where only the receiver has knowledge of the channel impulse
response. An approach for combining decision-feedback equalization with channel
coding is proposed, where decoding precedes the removal of intersymbol
interference. This is accomplished by combining the recently proposed
integer-forcing equalization approach with cyclic block codes. The channel
impulse response is linearly equalized to an integer-valued response. This is
then utilized by leveraging the property that a cyclic code is closed under
(cyclic) integer-valued convolution. Explicit bounds on the performance of the
proposed scheme are also derived
Communication Over MIMO Broadcast Channels Using Lattice-Basis Reduction
A simple scheme for communication over MIMO broadcast channels is introduced
which adopts the lattice reduction technique to improve the naive channel
inversion method. Lattice basis reduction helps us to reduce the average
transmitted energy by modifying the region which includes the constellation
points. Simulation results show that the proposed scheme performs well, and as
compared to the more complex methods (such as the perturbation method) has a
negligible loss. Moreover, the proposed method is extended to the case of
different rates for different users. The asymptotic behavior of the symbol
error rate of the proposed method and the perturbation technique, and also the
outage probability for the case of fixed-rate users is analyzed. It is shown
that the proposed method, based on LLL lattice reduction, achieves the optimum
asymptotic slope of symbol-error-rate (called the precoding diversity). Also,
the outage probability for the case of fixed sum-rate is analyzed.Comment: Submitted to IEEE Trans. on Info. Theory (Jan. 15, 2006), Revised
(Jun. 12, 2007
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