130,948 research outputs found
On Field Size and Success Probability in Network Coding
Using tools from algebraic geometry and Groebner basis theory we solve two
problems in network coding. First we present a method to determine the smallest
field size for which linear network coding is feasible. Second we derive
improved estimates on the success probability of random linear network coding.
These estimates take into account which monomials occur in the support of the
determinant of the product of Edmonds matrices. Therefore we finally
investigate which monomials can occur in the determinant of the Edmonds matrix.Comment: 16 pages, 3 figures, 2 tables. Accepted for publication at
International Workshop on the Arithmetic of Finite Fields, WAIFI 200
Random Linear Fountain Code with Improved Decoding Success Probability
In this paper we study the problem of increasing the decoding success
probability of random linear fountain code over GF(2) for small packet lengths
used in delay-intolerant applications such as multimedia streaming. Such code
over GF(2) are attractive as they have lower decoding complexity than codes
over larger field size, but suffer from high transmission redundancy. In our
proposed coding scheme we construct a codeword which is not a linear
combination of any codewords previously transmitted to mitigate such
transmission redundancy. We then note the observation that the probability of
receiving a linearly dependent codeword is highest when the receiver has
received k-1 linearly independent codewords. We propose using the BlockACK
frame so that the codeword received after k-1 linearly independent codeword is
always linearly independent, this reduces the expected redundancy by a factor
of three.Comment: This paper appears in: Communications (APCC), 2016 22nd Asia-Pacific
Conference o
A Network Coding Approach to Loss Tomography
Network tomography aims at inferring internal network characteristics based
on measurements at the edge of the network. In loss tomography, in particular,
the characteristic of interest is the loss rate of individual links and
multicast and/or unicast end-to-end probes are typically used. Independently,
recent advances in network coding have shown that there are advantages from
allowing intermediate nodes to process and combine, in addition to just
forward, packets. In this paper, we study the problem of loss tomography in
networks with network coding capabilities. We design a framework for estimating
link loss rates, which leverages network coding capabilities, and we show that
it improves several aspects of tomography including the identifiability of
links, the trade-off between estimation accuracy and bandwidth efficiency, and
the complexity of probe path selection. We discuss the cases of inferring link
loss rates in a tree topology and in a general topology. In the latter case,
the benefits of our approach are even more pronounced compared to standard
techniques, but we also face novel challenges, such as dealing with cycles and
multiple paths between sources and receivers. Overall, this work makes the
connection between active network tomography and network coding
Localized Dimension Growth in Random Network Coding: A Convolutional Approach
We propose an efficient Adaptive Random Convolutional Network Coding (ARCNC)
algorithm to address the issue of field size in random network coding. ARCNC
operates as a convolutional code, with the coefficients of local encoding
kernels chosen randomly over a small finite field. The lengths of local
encoding kernels increase with time until the global encoding kernel matrices
at related sink nodes all have full rank. Instead of estimating the necessary
field size a priori, ARCNC operates in a small finite field. It adapts to
unknown network topologies without prior knowledge, by locally incrementing the
dimensionality of the convolutional code. Because convolutional codes of
different constraint lengths can coexist in different portions of the network,
reductions in decoding delay and memory overheads can be achieved with ARCNC.
We show through analysis that this method performs no worse than random linear
network codes in general networks, and can provide significant gains in terms
of average decoding delay in combination networks.Comment: 7 pages, 1 figure, submitted to IEEE ISIT 201
Construction algorithm for network error-correcting codes attaining the Singleton bound
We give a centralized deterministic algorithm for constructing linear network
error-correcting codes that attain the Singleton bound of network
error-correcting codes. The proposed algorithm is based on the algorithm by
Jaggi et al. We give estimates on the time complexity and the required symbol
size of the proposed algorithm. We also estimate the probability of a random
choice of local encoding vectors by all intermediate nodes giving a network
error-correcting codes attaining the Singleton bound. We also clarify the
relationship between the robust network coding and the network error-correcting
codes with known locations of errors.Comment: To appear in IEICE Trans. Fundamentals
(http://ietfec.oxfordjournals.org/), vol. E90-A, no. 9, Sept. 2007. LaTeX2e,
7 pages, using ieice.cls and pstricks.sty. Version 4 adds randomized
construction of network error-correcting codes, comparisons of the proposed
methods to the existing methods, additional explanations in the proo
Improved Delay Estimates for a Queueing Model for Random Linear Coding for Unicast
Consider a lossy communication channel for unicast with zero-delay feedback.
For this communication scenario, a simple retransmission scheme is optimum with
respect to delay. An alternative approach is to use random linear coding in
automatic repeat-request (ARQ) mode. We extend the work of Shrader and
Ephremides, by deriving an expression for the delay of random linear coding
over field of infinite size. Simulation results for various field sizes are
also provided.Comment: 5 pages, 3 figures, accepted at the 2009 IEEE International Symposium
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