191,951 research outputs found
On network coding for sum-networks
A directed acyclic network is considered where all the terminals need to
recover the sum of the symbols generated at all the sources. We call such a
network a sum-network. It is shown that there exists a solvably (and linear
solvably) equivalent sum-network for any multiple-unicast network, and thus for
any directed acyclic communication network. It is also shown that there exists
a linear solvably equivalent multiple-unicast network for every sum-network. It
is shown that for any set of polynomials having integer coefficients, there
exists a sum-network which is scalar linear solvable over a finite field F if
and only if the polynomials have a common root in F. For any finite or cofinite
set of prime numbers, a network is constructed which has a vector linear
solution of any length if and only if the characteristic of the alphabet field
is in the given set. The insufficiency of linear network coding and
unachievability of the network coding capacity are proved for sum-networks by
using similar known results for communication networks. Under fractional vector
linear network coding, a sum-network and its reverse network are shown to be
equivalent. However, under non-linear coding, it is shown that there exists a
solvable sum-network whose reverse network is not solvable.Comment: Accepted to IEEE Transactions on Information Theor
Capacity of Sum-networks for Different Message Alphabets
A sum-network is a directed acyclic network in which all terminal nodes
demand the `sum' of the independent information observed at the source nodes.
Many characteristics of the well-studied multiple-unicast network communication
problem also hold for sum-networks due to a known reduction between instances
of these two problems. Our main result is that unlike a multiple unicast
network, the coding capacity of a sum-network is dependent on the message
alphabet. We demonstrate this using a construction procedure and show that the
choice of a message alphabet can reduce the coding capacity of a sum-network
from to close to
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
Computation in Multicast Networks: Function Alignment and Converse Theorems
The classical problem in network coding theory considers communication over
multicast networks. Multiple transmitters send independent messages to multiple
receivers which decode the same set of messages. In this work, computation over
multicast networks is considered: each receiver decodes an identical function
of the original messages. For a countably infinite class of two-transmitter
two-receiver single-hop linear deterministic networks, the computing capacity
is characterized for a linear function (modulo-2 sum) of Bernoulli sources.
Inspired by the geometric concept of interference alignment in networks, a new
achievable coding scheme called function alignment is introduced. A new
converse theorem is established that is tighter than cut-set based and
genie-aided bounds. Computation (vs. communication) over multicast networks
requires additional analysis to account for multiple receivers sharing a
network's computational resources. We also develop a network decomposition
theorem which identifies elementary parallel subnetworks that can constitute an
original network without loss of optimality. The decomposition theorem provides
a conceptually-simpler algebraic proof of achievability that generalizes to
-transmitter -receiver networks.Comment: to appear in the IEEE Transactions on Information Theor
Utility Optimal Coding for Packet Transmission over Wireless Networks - Part II: Networks of Packet Erasure Channels
We define a class of multi--hop erasure networks that approximates a wireless
multi--hop network. The network carries unicast flows for multiple users, and
each information packet within a flow is required to be decoded at the flow
destination within a specified delay deadline. The allocation of coding rates
amongst flows/users is constrained by network capacity. We propose a
proportional fair transmission scheme that maximises the sum utility of flow
throughputs. This is achieved by {\em jointly optimising the packet coding
rates and the allocation of bits of coded packets across transmission slots.}Comment: Submitted to the Forty-Ninth Annual Allerton Conference on
Communication, Control, and Computing, Monticello, Illinois, US
On Approximating the Sum-Rate for Multiple-Unicasts
We study upper bounds on the sum-rate of multiple-unicasts. We approximate
the Generalized Network Sharing Bound (GNS cut) of the multiple-unicasts
network coding problem with independent sources. Our approximation
algorithm runs in polynomial time and yields an upper bound on the joint source
entropy rate, which is within an factor from the GNS cut. It
further yields a vector-linear network code that achieves joint source entropy
rate within an factor from the GNS cut, but \emph{not} with
independent sources: the code induces a correlation pattern among the sources.
Our second contribution is establishing a separation result for vector-linear
network codes: for any given field there exist networks for which
the optimum sum-rate supported by vector-linear codes over for
independent sources can be multiplicatively separated by a factor of
, for any constant , from the optimum joint entropy
rate supported by a code that allows correlation between sources. Finally, we
establish a similar separation result for the asymmetric optimum vector-linear
sum-rates achieved over two distinct fields and
for independent sources, revealing that the choice of field
can heavily impact the performance of a linear network code.Comment: 10 pages; Shorter version appeared at ISIT (International Symposium
on Information Theory) 2015; some typos correcte
Utility Optimal Coding for Packet Transmission over Wireless Networks - Part I: Networks of Binary Symmetric Channels
We consider multi--hop networks comprising Binary Symmetric Channels
(s). The network carries unicast flows for multiple users. The
utility of the network is the sum of the utilities of the flows, where the
utility of each flow is a concave function of its throughput. Given that the
network capacity is shared by the flows, there is a contention for network
resources like coding rate (at the physical layer), scheduling time (at the MAC
layer), etc., among the flows. We propose a proportional fair transmission
scheme that maximises the sum utility of flow throughputs subject to the rate
and the scheduling constraints. This is achieved by {\em jointly optimising the
packet coding rates of all the flows through the network}.Comment: Submitted to Forty-Ninth Annual Allerton Conference on Communication,
Control, and Computing, Monticello, IL, US
Wireless Network Coding with Local Network Views: Coded Layer Scheduling
One of the fundamental challenges in the design of distributed wireless
networks is the large dynamic range of network state. Since continuous tracking
of global network state at all nodes is practically impossible, nodes can only
acquire limited local views of the whole network to design their transmission
strategies. In this paper, we study multi-layer wireless networks and assume
that each node has only a limited knowledge, namely 1-local view, where each
S-D pair has enough information to perform optimally when other pairs do not
interfere, along with connectivity information for rest of the network. We
investigate the information-theoretic limits of communication with such limited
knowledge at the nodes. We develop a novel transmission strategy, namely Coded
Layer Scheduling, that solely relies on 1-local view at the nodes and
incorporates three different techniques: (1) per layer interference avoidance,
(2) repetition coding to allow overhearing of the interference, and (3) network
coding to allow interference neutralization. We show that our proposed scheme
can provide a significant throughput gain compared with the conventional
interference avoidance strategies. Furthermore, we show that our strategy
maximizes the achievable normalized sum-rate for some classes of networks,
hence, characterizing the normalized sum-capacity of those networks with
1-local view.Comment: Technical report. A paper based on the results of this report will
appea
- …