7,365 research outputs found
Improving Distributed Gradient Descent Using Reed-Solomon Codes
Today's massively-sized datasets have made it necessary to often perform
computations on them in a distributed manner. In principle, a computational
task is divided into subtasks which are distributed over a cluster operated by
a taskmaster. One issue faced in practice is the delay incurred due to the
presence of slow machines, known as \emph{stragglers}. Several schemes,
including those based on replication, have been proposed in the literature to
mitigate the effects of stragglers and more recently, those inspired by coding
theory have begun to gain traction. In this work, we consider a distributed
gradient descent setting suitable for a wide class of machine learning
problems. We adapt the framework of Tandon et al. (arXiv:1612.03301) and
present a deterministic scheme that, for a prescribed per-machine computational
effort, recovers the gradient from the least number of machines
theoretically permissible, via an decoding algorithm. We also provide
a theoretical delay model which can be used to minimize the expected waiting
time per computation by optimally choosing the parameters of the scheme.
Finally, we supplement our theoretical findings with numerical results that
demonstrate the efficacy of the method and its advantages over competing
schemes
On the Performance of Short Block Codes over Finite-State Channels in the Rare-Transition Regime
As the mobile application landscape expands, wireless networks are tasked
with supporting different connection profiles, including real-time traffic and
delay-sensitive communications. Among many ensuing engineering challenges is
the need to better understand the fundamental limits of forward error
correction in non-asymptotic regimes. This article characterizes the
performance of random block codes over finite-state channels and evaluates
their queueing performance under maximum-likelihood decoding. In particular,
classical results from information theory are revisited in the context of
channels with rare transitions, and bounds on the probabilities of decoding
failure are derived for random codes. This creates an analysis framework where
channel dependencies within and across codewords are preserved. Such results
are subsequently integrated into a queueing problem formulation. For instance,
it is shown that, for random coding on the Gilbert-Elliott channel, the
performance analysis based on upper bounds on error probability provides very
good estimates of system performance and optimum code parameters. Overall, this
study offers new insights about the impact of channel correlation on the
performance of delay-aware, point-to-point communication links. It also
provides novel guidelines on how to select code rates and block lengths for
real-time traffic over wireless communication infrastructures
V2X Content Distribution Based on Batched Network Coding with Distributed Scheduling
Content distribution is an application in intelligent transportation system
to assist vehicles in acquiring information such as digital maps and
entertainment materials. In this paper, we consider content distribution from a
single roadside infrastructure unit to a group of vehicles passing by it. To
combat the short connection time and the lossy channel quality, the downloaded
contents need to be further shared among vehicles after the initial
broadcasting phase. To this end, we propose a joint infrastructure-to-vehicle
(I2V) and vehicle-to-vehicle (V2V) communication scheme based on batched sparse
(BATS) coding to minimize the traffic overhead and reduce the total
transmission delay. In the I2V phase, the roadside unit (RSU) encodes the
original large-size file into a number of batches in a rateless manner, each
containing a fixed number of coded packets, and sequentially broadcasts them
during the I2V connection time. In the V2V phase, vehicles perform the network
coded cooperative sharing by re-encoding the received packets. We propose a
utility-based distributed algorithm to efficiently schedule the V2V cooperative
transmissions, hence reducing the transmission delay. A closed-form expression
for the expected rank distribution of the proposed content distribution scheme
is derived, which is used to design the optimal BATS code. The performance of
the proposed content distribution scheme is evaluated by extensive simulations
that consider multi-lane road and realistic vehicular traffic settings, and
shown to significantly outperform the existing content distribution protocols.Comment: 12 pages and 9 figure
Expander Chunked Codes
Chunked codes are efficient random linear network coding (RLNC) schemes with
low computational cost, where the input packets are encoded into small chunks
(i.e., subsets of the coded packets). During the network transmission, RLNC is
performed within each chunk. In this paper, we first introduce a simple
transfer matrix model to characterize the transmission of chunks, and derive
some basic properties of the model to facilitate the performance analysis. We
then focus on the design of overlapped chunked codes, a class of chunked codes
whose chunks are non-disjoint subsets of input packets, which are of special
interest since they can be encoded with negligible computational cost and in a
causal fashion. We propose expander chunked (EC) codes, the first class of
overlapped chunked codes that have an analyzable performance,where the
construction of the chunks makes use of regular graphs. Numerical and
simulation results show that in some practical settings, EC codes can achieve
rates within 91 to 97 percent of the optimum and outperform the
state-of-the-art overlapped chunked codes significantly.Comment: 26 pages, 3 figures, submitted for journal publicatio
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