2 research outputs found
Binary error correcting network codes
We consider network coding for networks experiencing worst-case bit-flip
errors, and 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. We propose a new metric for errors under this model. Using
this metric, we prove a new Hamming-type upper bound on the network capacity.
We also show a commensurate lower bound based on GV-type codes that can be used
for error-correction. The codes used to attain the lower bound are non-coherent
(do not require prior knowledge of network topology). The end-to-end nature of
our design enables our codes to be overlaid on classical distributed random
linear network codes. Further, we free internal nodes from having to implement
potentially computationally intensive link-by-link error-correction
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