2,379 research outputs found
Limit groups are CAT(0)
We prove that every limit group acts geometrically on a CAT(0) space with the
isolated flats property.Comment: The statement of Main theorem is improved, and the proof is changed
accordingly. Minor changes to expositio
Effects of the Generation Size and Overlap on Throughput and Complexity in Randomized Linear Network Coding
To reduce computational complexity and delay in randomized network coded
content distribution, and for some other practical reasons, coding is not
performed simultaneously over all content blocks, but over much smaller,
possibly overlapping subsets of these blocks, known as generations. A penalty
of this strategy is throughput reduction. To analyze the throughput loss, we
model coding over generations with random generation scheduling as a coupon
collector's brotherhood problem. This model enables us to derive the expected
number of coded packets needed for successful decoding of the entire content as
well as the probability of decoding failure (the latter only when generations
do not overlap) and further, to quantify the tradeoff between computational
complexity and throughput. Interestingly, with a moderate increase in the
generation size, throughput quickly approaches link capacity. Overlaps between
generations can further improve throughput substantially for relatively small
generation sizes.Comment: To appear in IEEE Transactions on Information Theory Special Issue:
Facets of Coding Theory: From Algorithms to Networks, Feb 201
Coding for Fast Content Download
We study the fundamental trade-off between storage and content download time.
We show that the download time can be significantly reduced by dividing the
content into chunks, encoding it to add redundancy and then distributing it
across multiple disks. We determine the download time for two content access
models - the fountain and fork-join models that involve simultaneous content
access, and individual access from enqueued user requests respectively. For the
fountain model we explicitly characterize the download time, while in the
fork-join model we derive the upper and lower bounds. Our results show that
coding reduces download time, through the diversity of distributing the data
across more disks, even for the total storage used.Comment: 8 pages, 6 figures, conferenc
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