87 research outputs found
Streaming Codes for Channels with Burst and Isolated Erasures
We study low-delay error correction codes for streaming recovery over a class
of packet-erasure channels that introduce both burst-erasures and isolated
erasures. We propose a simple, yet effective class of codes whose parameters
can be tuned to obtain a tradeoff between the capability to correct burst and
isolated erasures. Our construction generalizes previously proposed low-delay
codes which are effective only against burst erasures. We establish an
information theoretic upper bound on the capability of any code to
simultaneously correct burst and isolated erasures and show that our proposed
constructions meet the upper bound in some special cases. We discuss the
operational significance of column-distance and column-span metrics and
establish that the rate 1/2 codes discovered by Martinian and Sundberg [IT
Trans.\, 2004] through a computer search indeed attain the optimal
column-distance and column-span tradeoff. Numerical simulations over a
Gilbert-Elliott channel model and a Fritchman model show significant
performance gains over previously proposed low-delay codes and random linear
codes for certain range of channel parameters
Rate-Optimal Streaming Codes for Channels with Burst and Isolated Erasures
Recovery of data packets from packet erasures in a timely manner is critical
for many streaming applications. An early paper by Martinian and Sundberg
introduced a framework for streaming codes and designed rate-optimal codes that
permit delay-constrained recovery from an erasure burst of length up to . A
recent work by Badr et al. extended this result and introduced a sliding-window
channel model . Under this model, in a sliding-window of
width , one of the following erasure patterns are possible (i) a burst of
length at most or (ii) at most (possibly non-contiguous) arbitrary
erasures. Badr et al. obtained a rate upper bound for streaming codes that can
recover with a time delay , from any erasure patterns permissible under the
model. However, constructions matching the bound were
absent, except for a few parameter sets. In this paper, we present an explicit
family of codes that achieves the rate upper bound for all feasible parameters
, , and .Comment: shorter version submitted to ISIT 201
Multiplexed Streaming Codes for Messages With Different Decoding Delays in Channel with Burst and Random Erasures
In a real-time transmission scenario, messages are transmitted through a
channel that is subject to packet loss. The destination must recover the
messages within the required deadline. In this paper, we consider a setup where
two different types of messages with distinct decoding deadlines are
transmitted through a channel that can introduce burst erasures of a length at
most , or random erasures. The message with a short decoding deadline
is referred to as an urgent message, while the other one with a decoding
deadline () is referred to as a less urgent message.
We propose a merging method to encode two message streams of different
urgency levels into a single flow. We consider the scenario where . We establish that any coding strategy based on this merging approach has a
closed-form upper limit on its achievable sum rate. Moreover, we present
explicit constructions within a finite field that scales quadratically with the
imposed delay, ensuring adherence to the upper bound. In a given parameter
configuration, we rigorously demonstrate that the sum rate of our proposed
streaming codes consistently surpasses that of separate encoding, which serves
as a baseline for comparison
Private Streaming with Convolutional Codes
Recently, information-theoretic private information retrieval (PIR) from
coded storage systems has gained a lot of attention, and a general star product
PIR scheme was proposed. In this paper, the star product scheme is adopted,
with appropriate modifications, to the case of private (e.g., video) streaming.
It is assumed that the files to be streamed are stored on~ servers in a
coded form, and the streaming is carried out via a convolutional code. The star
product scheme is defined for this special case, and various properties are
analyzed for two channel models related to straggling and Byzantine servers,
both in the baseline case as well as with colluding servers. The achieved PIR
rates for the given models are derived and, for the cases where the capacity is
known, the first model is shown to be asymptotically optimal, when the number
of stripes in a file is large. The second scheme introduced in this work is
shown to be the equivalent of block convolutional codes in the PIR setting. For
the Byzantine server model, it is shown to outperform the trivial scheme of
downloading stripes of the desired file separately without memory
Online Versus Offline Rate in Streaming Codes for Variable-Size Messages
Providing high quality-of-service for live communication is a pervasive
challenge which is plagued by packet losses during transmission. Streaming
codes are a class of erasure codes specifically designed for such low-latency
streaming communication settings. We consider the recently proposed setting of
streaming codes under variable-size messages which reflects the requirements of
applications such as live video streaming. In practice, streaming codes often
need to operate in an "online" setting where the sizes of the future messages
are unknown. Yet, previously studied upper bounds on the rate apply to
"offline" coding schemes with access to all (including future) message sizes.
In this paper, we evaluate whether the optimal offline rate is a feasible
goal for online streaming codes when communicating over a burst-only packet
loss channel. We identify two broad parameter regimes where, perhaps
surprisingly, online streaming codes can, in fact, match the optimal offline
rate. For both of these settings, we present rate-optimal online code
constructions. For all remaining parameter settings, we establish that it is
impossible for online coding schemes to attain the optimal offline rate.Comment: 16 pages, 2 figures, this is an extended version of the IEEE ISIT
2020 paper with the same titl
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