17 research outputs found
On the Delay of Network Coding over Line Networks
We analyze a simple network where a source and a receiver are connected by a
line of erasure channels of different reliabilities. Recent prior work has
shown that random linear network coding can achieve the min-cut capacity and
therefore the asymptotic rate is determined by the worst link of the line
network. In this paper we investigate the delay for transmitting a batch of
packets, which is a function of all the erasure probabilities and the number of
packets in the batch. We show a monotonicity result on the delay function and
derive simple expressions which characterize the expected delay behavior of
line networks. Further, we use a martingale bounded differences argument to
show that the actual delay is tightly concentrated around its expectation
When Queueing Meets Coding: Optimal-Latency Data Retrieving Scheme in Storage Clouds
In this paper, we study the problem of reducing the delay of downloading data
from cloud storage systems by leveraging multiple parallel threads, assuming
that the data has been encoded and stored in the clouds using fixed rate
forward error correction (FEC) codes with parameters (n, k). That is, each file
is divided into k equal-sized chunks, which are then expanded into n chunks
such that any k chunks out of the n are sufficient to successfully restore the
original file. The model can be depicted as a multiple-server queue with
arrivals of data retrieving requests and a server corresponding to a thread.
However, this is not a typical queueing model because a server can terminate
its operation, depending on when other servers complete their service (due to
the redundancy that is spread across the threads). Hence, to the best of our
knowledge, the analysis of this queueing model remains quite uncharted.
Recent traces from Amazon S3 show that the time to retrieve a fixed size
chunk is random and can be approximated as a constant delay plus an i.i.d.
exponentially distributed random variable. For the tractability of the
theoretical analysis, we assume that the chunk downloading time is i.i.d.
exponentially distributed. Under this assumption, we show that any
work-conserving scheme is delay-optimal among all on-line scheduling schemes
when k = 1. When k > 1, we find that a simple greedy scheme, which allocates
all available threads to the head of line request, is delay optimal among all
on-line scheduling schemes. We also provide some numerical results that point
to the limitations of the exponential assumption, and suggest further research
directions.Comment: Original accepted by IEEE Infocom 2014, 9 pages. Some statements in
the Infocom paper are correcte
How Fast Can Dense Codes Achieve the Min-Cut Capacity of Line Networks?
In this paper, we study the coding delay and the average coding delay of
random linear network codes (dense codes) over line networks with deterministic
regular and Poisson transmission schedules. We consider both lossless networks
and networks with Bernoulli losses. The upper bounds derived in this paper,
which are in some cases more general, and in some other cases tighter, than the
existing bounds, provide a more clear picture of the speed of convergence of
dense codes to the min-cut capacity of line networks.Comment: 15 pages, submitted to IEEE ISIT 201
In-Order Delivery Delay of Transport Layer Coding
A large number of streaming applications use reliable transport protocols
such as TCP to deliver content over the Internet. However, head-of-line
blocking due to packet loss recovery can often result in unwanted behavior and
poor application layer performance. Transport layer coding can help mitigate
this issue by helping to recover from lost packets without waiting for
retransmissions. We consider the use of an on-line network code that inserts
coded packets at strategic locations within the underlying packet stream. If
retransmissions are necessary, additional coding packets are transmitted to
ensure the receiver's ability to decode. An analysis of this scheme is provided
that helps determine both the expected in-order packet delivery delay and its
variance. Numerical results are then used to determine when and how many coded
packets should be inserted into the packet stream, in addition to determining
the trade-offs between reducing the in-order delay and the achievable rate. The
analytical results are finally compared with experimental results to provide
insight into how to minimize the delay of existing transport layer protocols
TOFEC: Achieving Optimal Throughput-Delay Trade-off of Cloud Storage Using Erasure Codes
Our paper presents solutions using erasure coding, parallel connections to
storage cloud and limited chunking (i.e., dividing the object into a few
smaller segments) together to significantly improve the delay performance of
uploading and downloading data in and out of cloud storage.
TOFEC is a strategy that helps front-end proxy adapt to level of workload by
treating scalable cloud storage (e.g. Amazon S3) as a shared resource requiring
admission control. Under light workloads, TOFEC creates more smaller chunks and
uses more parallel connections per file, minimizing service delay. Under heavy
workloads, TOFEC automatically reduces the level of chunking (fewer chunks with
increased size) and uses fewer parallel connections to reduce overhead,
resulting in higher throughput and preventing queueing delay. Our trace-driven
simulation results show that TOFEC's adaptation mechanism converges to an
appropriate code that provides the optimal delay-throughput trade-off without
reducing system capacity. Compared to a non-adaptive strategy optimized for
throughput, TOFEC delivers 2.5x lower latency under light workloads; compared
to a non-adaptive strategy optimized for latency, TOFEC can scale to support
over 3x as many requests
Minimum cost mirror sites using network coding: Replication vs. coding at the source nodes
Content distribution over networks is often achieved by using mirror sites
that hold copies of files or portions thereof to avoid congestion and delay
issues arising from excessive demands to a single location. Accordingly, there
are distributed storage solutions that divide the file into pieces and place
copies of the pieces (replication) or coded versions of the pieces (coding) at
multiple source nodes. We consider a network which uses network coding for
multicasting the file. There is a set of source nodes that contains either
subsets or coded versions of the pieces of the file. The cost of a given
storage solution is defined as the sum of the storage cost and the cost of the
flows required to support the multicast. Our interest is in finding the storage
capacities and flows at minimum combined cost. We formulate the corresponding
optimization problems by using the theory of information measures. In
particular, we show that when there are two source nodes, there is no loss in
considering subset sources. For three source nodes, we derive a tight upper
bound on the cost gap between the coded and uncoded cases. We also present
algorithms for determining the content of the source nodes.Comment: IEEE Trans. on Information Theory (to appear), 201