649 research outputs found
Nested Lattice Codes for Gaussian Relay Networks with Interference
In this paper, a class of relay networks is considered. We assume that, at a
node, outgoing channels to its neighbors are orthogonal, while incoming signals
from neighbors can interfere with each other. We are interested in the
multicast capacity of these networks. As a subclass, we first focus on Gaussian
relay networks with interference and find an achievable rate using a lattice
coding scheme. It is shown that there is a constant gap between our achievable
rate and the information theoretic cut-set bound. This is similar to the recent
result by Avestimehr, Diggavi, and Tse, who showed such an approximate
characterization of the capacity of general Gaussian relay networks. However,
our achievability uses a structured code instead of a random one. Using the
same idea used in the Gaussian case, we also consider linear finite-field
symmetric networks with interference and characterize the capacity using a
linear coding scheme.Comment: 23 pages, 5 figures, submitted to IEEE Transactions on Information
Theor
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
CFMA (Compute-Forward Multiple Access) and its Applications in Network Information Theory
While both fundamental limits and system implementations are well understood for the point-to-point communication system, much less is developed for general communication networks. This thesis contributes towards the design and analysis of advanced coding schemes for multi-user communication networks with structured codes. The first part of the thesis investigates the usefulness of lattice codes in Gaussian networks with a generalized compute-and-forward scheme. As an application, we introduce a novel multiple access technique --- Compute-Forward Multiple Access (CFMA), and show that it achieves the capacity region of the Gaussian multiple access channel (MAC) with low receiver complexities. Similar coding schemes are also devised for other multi-user networks, including the Gaussian MAC with states, the two-way relay channel, the many-to-one interference channel, etc., demonstrating improvements of system performance because of the good interference mitigation property of lattice codes. As a common theme in the thesis, computing the sum of codewords over a Gaussian MAC is of particular theoretical importance. We study this problem with nested linear codes, and improve upon the currently best known results obtained by nested lattice codes. Inspired by the advantages of linear and lattice codes in Gaussian networks, we make a further step towards understanding intrinsic properties of the sum of linear codes. The final part of the thesis introduces the notion of typical sumset and presents asymptotic results on the typical sumset size of linear codes. The results offer new insight to coding schemes with structured codes
Compute-and-Forward: Harnessing Interference through Structured Codes
Interference is usually viewed as an obstacle to communication in wireless
networks. This paper proposes a new strategy, compute-and-forward, that
exploits interference to obtain significantly higher rates between users in a
network. The key idea is that relays should decode linear functions of
transmitted messages according to their observed channel coefficients rather
than ignoring the interference as noise. After decoding these linear equations,
the relays simply send them towards the destinations, which given enough
equations, can recover their desired messages. The underlying codes are based
on nested lattices whose algebraic structure ensures that integer combinations
of codewords can be decoded reliably. Encoders map messages from a finite field
to a lattice and decoders recover equations of lattice points which are then
mapped back to equations over the finite field. This scheme is applicable even
if the transmitters lack channel state information.Comment: IEEE Trans. Info Theory, to appear. 23 pages, 13 figure
Reliable Physical Layer Network Coding
When two or more users in a wireless network transmit simultaneously, their
electromagnetic signals are linearly superimposed on the channel. As a result,
a receiver that is interested in one of these signals sees the others as
unwanted interference. This property of the wireless medium is typically viewed
as a hindrance to reliable communication over a network. However, using a
recently developed coding strategy, interference can in fact be harnessed for
network coding. In a wired network, (linear) network coding refers to each
intermediate node taking its received packets, computing a linear combination
over a finite field, and forwarding the outcome towards the destinations. Then,
given an appropriate set of linear combinations, a destination can solve for
its desired packets. For certain topologies, this strategy can attain
significantly higher throughputs over routing-based strategies. Reliable
physical layer network coding takes this idea one step further: using
judiciously chosen linear error-correcting codes, intermediate nodes in a
wireless network can directly recover linear combinations of the packets from
the observed noisy superpositions of transmitted signals. Starting with some
simple examples, this survey explores the core ideas behind this new technique
and the possibilities it offers for communication over interference-limited
wireless networks.Comment: 19 pages, 14 figures, survey paper to appear in Proceedings of the
IEE
The Multi-way Relay Channel
The multiuser communication channel, in which multiple users exchange
information with the help of a relay terminal, termed the multi-way relay
channel (mRC), is introduced. In this model, multiple interfering clusters of
users communicate simultaneously, where the users within the same cluster wish
to exchange messages among themselves. It is assumed that the users cannot
receive each other's signals directly, and hence the relay terminal in this
model is the enabler of communication. In particular, restricted encoders,
which ignore the received channel output and use only the corresponding
messages for generating the channel input, are considered. Achievable rate
regions and an outer bound are characterized for the Gaussian mRC, and their
comparison is presented in terms of exchange rates in a symmetric Gaussian
network scenario. It is shown that the compress-and-forward (CF) protocol
achieves exchange rates within a constant bit offset of the exchange capacity
independent of the power constraints of the terminals in the network. A finite
bit gap between the exchange rates achieved by the CF and the
amplify-and-forward (AF) protocols is also shown. The two special cases of the
mRC, the full data exchange model, in which every user wants to receive
messages of all other users, and the pairwise data exchange model which
consists of multiple two-way relay channels, are investigated in detail. In
particular for the pairwise data exchange model, in addition to the proposed
random coding based achievable schemes, a nested lattice coding based scheme is
also presented and is shown to achieve exchange rates within a constant bit gap
of the exchange capacity.Comment: Revised version of our submission to the Transactions on Information
Theor
Lattice Coding for the Two-way Two-relay Channel
Lattice coding techniques may be used to derive achievable rate regions which
outperform known independent, identically distributed (i.i.d.) random codes in
multi-source relay networks and in particular the two-way relay channel. Gains
stem from the ability to decode the sum of codewords (or messages) using
lattice codes at higher rates than possible with i.i.d. random codes. Here we
develop a novel lattice coding scheme for the Two-way Two-relay Channel: 1
2 3 4, where Node 1 and 4 simultaneously communicate with each other
through two relay nodes 2 and 3. Each node only communicates with its
neighboring nodes. The key technical contribution is the lattice-based
achievability strategy, where each relay is able to remove the noise while
decoding the sum of several signals in a Block Markov strategy and then
re-encode the signal into another lattice codeword using the so-called
"Re-distribution Transform". This allows nodes further down the line to again
decode sums of lattice codewords. This transform is central to improving the
achievable rates, and ensures that the messages traveling in each of the two
directions fully utilize the relay's power, even under asymmetric channel
conditions. All decoders are lattice decoders and only a single nested lattice
codebook pair is needed. The symmetric rate achieved by the proposed lattice
coding scheme is within 0.5 log 3 bit/Hz/s of the symmetric rate capacity.Comment: submitted to IEEE Transactions on Information Theory on December 3,
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
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