182,273 research outputs found
Gaussian Multiple Access via Compute-and-Forward
Lattice codes used under the Compute-and-Forward paradigm suggest an
alternative strategy for the standard Gaussian multiple-access channel (MAC):
The receiver successively decodes integer linear combinations of the messages
until it can invert and recover all messages. In this paper, a multiple-access
technique called CFMA (Compute-Forward Multiple Access) is proposed and
analyzed. For the two-user MAC, it is shown that without time-sharing, the
entire capacity region can be attained using CFMA with a single-user decoder as
soon as the signal-to-noise ratios are above . A partial analysis
is given for more than two users. Lastly the strategy is extended to the
so-called dirty MAC where two interfering signals are known non-causally to the
two transmitters in a distributed fashion. Our scheme extends the previously
known results and gives new achievable rate regions.Comment: to appear in IEEE Transactions on Information Theor
Weak Secrecy in the Multi-Way Untrusted Relay Channel with Compute-and-Forward
We investigate the problem of secure communications in a Gaussian multi-way
relay channel applying the compute-and-forward scheme using nested lattice
codes. All nodes employ half-duplex operation and can exchange confidential
messages only via an untrusted relay. The relay is assumed to be honest but
curious, i.e., an eavesdropper that conforms to the system rules and applies
the intended relaying scheme. We start with the general case of the
single-input multiple-output (SIMO) L-user multi-way relay channel and provide
an achievable secrecy rate region under a weak secrecy criterion. We show that
the securely achievable sum rate is equivalent to the difference between the
computation rate and the multiple access channel (MAC) capacity. Particularly,
we show that all nodes must encode their messages such that the common
computation rate tuple falls outside the MAC capacity region of the relay. We
provide results for the single-input single-output (SISO) and the
multiple-input single-input (MISO) L-user multi-way relay channel as well as
the two-way relay channel. We discuss these results and show the dependency
between channel realization and achievable secrecy rate. We further compare our
result to available results in the literature for different schemes and show
that the proposed scheme operates close to the compute-and-forward rate without
secrecy.Comment: submitted to JSAC Special Issue on Fundamental Approaches to Network
Coding in Wireless Communication System
Lossy Compression for Compute-and-Forward in Limited Backhaul Uplink Multicell Processing
We study the transmission over a cloud radio access network in which multiple
base stations (BS) are connected to a central processor (CP) via
finite-capacity backhaul links. We propose two lattice-based coding schemes. In
the first scheme, the base stations decode linear combinations of the
transmitted messages, in the spirit of compute-and-forward (CoF), but differs
from it essentially in that the decoded equations are remapped to linear
combinations of the channel input symbols, sent compressed in a lossy manner to
the central processor, and are not required to be linearly independent. Also,
by opposition to the standard CoF, an appropriate multi-user decoder is
utilized to recover the sent messages. The second coding scheme generalizes the
first one by also allowing, at each relay node, a joint compression of the
decoded equation and the received signal. Both schemes apply in general, but
are more suited for situations in which there are more users than base
stations. We show that both schemes can outperform standard CoF and successive
Wyner-Ziv schemes in certain regimes, and illustrate the gains through some
numerical examples.Comment: Submitted to IEEE Transactions on Communication
Cooperative Compute-and-Forward
We examine the benefits of user cooperation under compute-and-forward. Much
like in network coding, receivers in a compute-and-forward network recover
finite-field linear combinations of transmitters' messages. Recovery is enabled
by linear codes: transmitters map messages to a linear codebook, and receivers
attempt to decode the incoming superposition of signals to an integer
combination of codewords. However, the achievable computation rates are low if
channel gains do not correspond to a suitable linear combination. In response
to this challenge, we propose a cooperative approach to compute-and-forward. We
devise a lattice-coding approach to block Markov encoding with which we
construct a decode-and-forward style computation strategy. Transmitters
broadcast lattice codewords, decode each other's messages, and then
cooperatively transmit resolution information to aid receivers in decoding the
integer combinations. Using our strategy, we show that cooperation offers a
significant improvement both in the achievable computation rate and in the
diversity-multiplexing tradeoff.Comment: submitted to IEEE Transactions on Information Theor
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
Computation Over Gaussian Networks With Orthogonal Components
Function computation of arbitrarily correlated discrete sources over Gaussian
networks with orthogonal components is studied. Two classes of functions are
considered: the arithmetic sum function and the type function. The arithmetic
sum function in this paper is defined as a set of multiple weighted arithmetic
sums, which includes averaging of the sources and estimating each of the
sources as special cases. The type or frequency histogram function counts the
number of occurrences of each argument, which yields many important statistics
such as mean, variance, maximum, minimum, median, and so on. The proposed
computation coding first abstracts Gaussian networks into the corresponding
modulo sum multiple-access channels via nested lattice codes and linear network
coding and then computes the desired function by using linear Slepian-Wolf
source coding. For orthogonal Gaussian networks (with no broadcast and
multiple-access components), the computation capacity is characterized for a
class of networks. For Gaussian networks with multiple-access components (but
no broadcast), an approximate computation capacity is characterized for a class
of networks.Comment: 30 pages, 12 figures, submitted to IEEE Transactions on Information
Theor
Signal-Aligned Network Coding in K-User MIMO Interference Channels with Limited Receiver Cooperation
In this paper, we propose a signal-aligned network coding (SNC) scheme for
K-user time-varying multiple-input multiple-output (MIMO) interference channels
with limited receiver cooperation. We assume that the receivers are connected
to a central processor via wired cooperation links with individual limited
capacities. Our SNC scheme determines the precoding matrices of the
transmitters so that the transmitted signals are aligned at each receiver. The
aligned signals are then decoded into noiseless integer combinations of
messages, also known as network-coded messages, by physical-layer network
coding. The key idea of our scheme is to ensure that independent integer
combinations of messages can be decoded at the receivers. Hence the central
processor can recover the original messages of the transmitters by solving the
linearly independent equations. We prove that our SNC scheme achieves full
degrees of freedom (DoF) by utilizing signal alignment and physical-layer
network coding. Simulation results show that our SNC scheme outperforms the
compute-and-forward scheme in the finite SNR regime of the two-user and the
three-user cases. The performance improvement of our SNC scheme mainly comes
from efficient utilization of the signal subspaces for conveying independent
linear equations of messages to the central processor.Comment: 12 pages, 4 figures, submitted to the IEEE Transactions on Vehicular
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