1,772 research outputs found
Refined Coding Bounds and Code Constructions for Coherent Network Error Correction
Coherent network error correction is the error-control problem in network
coding with the knowledge of the network codes at the source and sink nodes.
With respect to a given set of local encoding kernels defining a linear network
code, we obtain refined versions of the Hamming bound, the Singleton bound and
the Gilbert-Varshamov bound for coherent network error correction. Similar to
its classical counterpart, this refined Singleton bound is tight for linear
network codes. The tightness of this refined bound is shown by two construction
algorithms of linear network codes achieving this bound. These two algorithms
illustrate different design methods: one makes use of existing network coding
algorithms for error-free transmission and the other makes use of classical
error-correcting codes. The implication of the tightness of the refined
Singleton bound is that the sink nodes with higher maximum flow values can have
higher error correction capabilities.Comment: 32 page
End-to-End Error-Correcting Codes on Networks with Worst-Case Symbol Errors
The problem of coding for networks experiencing worst-case symbol errors is
considered. We argue that this is a reasonable model for highly dynamic
wireless network transmissions. We demonstrate that in this setup prior network
error-correcting schemes can be arbitrarily far from achieving the optimal
network throughput. A new transform metric for errors under the considered
model is proposed. Using this metric, we replicate many of the classical
results from coding theory. Specifically, we prove new Hamming-type,
Plotkin-type, and Elias-Bassalygo-type upper bounds on the network capacity. A
commensurate lower bound is shown based on Gilbert-Varshamov-type codes for
error-correction. The GV codes used to attain the lower bound can be
non-coherent, that is, they do not require prior knowledge of the network
topology. We also propose a computationally-efficient concatenation scheme. The
rate achieved by our concatenated codes is characterized by a Zyablov-type
lower bound. We provide a generalized minimum-distance decoding algorithm which
decodes up to half the minimum distance of the concatenated codes. The
end-to-end nature of our design enables our codes to be overlaid on the
classical distributed random linear network codes [1]. Furthermore, the
potentially intensive computation at internal nodes for the link-by-link
error-correction is un-necessary based on our design.Comment: Submitted for publication. arXiv admin note: substantial text overlap
with arXiv:1108.239
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