660 research outputs found
Approaching Gaussian Relay Network Capacity in the High SNR Regime: End-to-End Lattice Codes
We present a natural and low-complexity technique for achieving the capacity
of the Gaussian relay network in the high SNR regime. Specifically, we propose
the use of end-to-end structured lattice codes with the amplify-and-forward
strategy, where the source uses a nested lattice code to encode the messages
and the destination decodes the messages by lattice decoding. All intermediate
relays simply amplify and forward the received signals over the network to the
destination. We show that the end-to-end lattice-coded amplify-and-forward
scheme approaches the capacity of the layered Gaussian relay network in the
high SNR regime. Next, we extend our scheme to non-layered Gaussian relay
networks under the amplify-and-forward scheme, which can be viewed as a
Gaussian intersymbol interference (ISI) channel. Compared with other schemes,
our approach is significantly simpler and requires only the end-to-end design
of the lattice precoding and decoding. It does not require any knowledge of the
network topology or the individual channel gains
Construction of Capacity-Achieving Lattice Codes: Polar Lattices
In this paper, we propose a new class of lattices constructed from polar
codes, namely polar lattices, to achieve the capacity \frac{1}{2}\log(1+\SNR)
of the additive white Gaussian-noise (AWGN) channel. Our construction follows
the multilevel approach of Forney \textit{et al.}, where we construct a
capacity-achieving polar code on each level. The component polar codes are
shown to be naturally nested, thereby fulfilling the requirement of the
multilevel lattice construction. We prove that polar lattices are
\emph{AWGN-good}. Furthermore, using the technique of source polarization, we
propose discrete Gaussian shaping over the polar lattice to satisfy the power
constraint. Both the construction and shaping are explicit, and the overall
complexity of encoding and decoding is for any fixed target error
probability.Comment: full version of the paper to appear in IEEE Trans. Communication
Sparse Regression Codes for Multi-terminal Source and Channel Coding
We study a new class of codes for Gaussian multi-terminal source and channel
coding. These codes are designed using the statistical framework of
high-dimensional linear regression and are called Sparse Superposition or
Sparse Regression codes. Codewords are linear combinations of subsets of
columns of a design matrix. These codes were recently introduced by Barron and
Joseph and shown to achieve the channel capacity of AWGN channels with
computationally feasible decoding. They have also recently been shown to
achieve the optimal rate-distortion function for Gaussian sources. In this
paper, we demonstrate how to implement random binning and superposition coding
using sparse regression codes. In particular, with minimum-distance
encoding/decoding it is shown that sparse regression codes attain the optimal
information-theoretic limits for a variety of multi-terminal source and channel
coding problems.Comment: 9 pages, appeared in the Proceedings of the 50th Annual Allerton
Conference on Communication, Control, and Computing - 201
On Achievable Rate Regions of the Asymmetric AWGN Two-Way Relay Channel
This paper investigates the additive white Gaussian noise two-way relay
channel, where two users exchange messages through a relay. Asymmetrical
channels are considered where the users can transmit data at different rates
and at different power levels. We modify and improve existing coding schemes to
obtain three new achievable rate regions. Comparing four downlink-optimal
coding schemes, we show that the scheme that gives the best sum-rate
performance is (i) complete-decode-forward, when both users transmit at low
signal-to-noise ratio (SNR); (ii) functional-decode-forward with nested lattice
codes, when both users transmit at high SNR; (iii) functional-decode-forward
with rate splitting and time-division multiplexing, when one user transmits at
low SNR and another user at medium--high SNR.Comment: to be presented at ISIT 201
Integer-Forcing Source Coding
Integer-Forcing (IF) is a new framework, based on compute-and-forward, for
decoding multiple integer linear combinations from the output of a Gaussian
multiple-input multiple-output channel. This work applies the IF approach to
arrive at a new low-complexity scheme, IF source coding, for distributed lossy
compression of correlated Gaussian sources under a minimum mean squared error
distortion measure. All encoders use the same nested lattice codebook. Each
encoder quantizes its observation using the fine lattice as a quantizer and
reduces the result modulo the coarse lattice, which plays the role of binning.
Rather than directly recovering the individual quantized signals, the decoder
first recovers a full-rank set of judiciously chosen integer linear
combinations of the quantized signals, and then inverts it. In general, the
linear combinations have smaller average powers than the original signals. This
allows to increase the density of the coarse lattice, which in turn translates
to smaller compression rates. We also propose and analyze a one-shot version of
IF source coding, that is simple enough to potentially lead to a new design
principle for analog-to-digital converters that can exploit spatial
correlations between the sampled signals.Comment: Submitted to IEEE Transactions on Information Theor
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