17 research outputs found
Erasure Coding for Real-Time Streaming
We consider a real-time streaming system where messages are created
sequentially at the source, and are encoded for transmission to the receiver
over a packet erasure link. Each message must subsequently be decoded at the
receiver within a given delay from its creation time. The goal is to construct
an erasure correction code that achieves the maximum message size when all
messages must be decoded by their respective deadlines under a specified set of
erasure patterns (erasure model). We present an explicit intrasession code
construction that is asymptotically optimal under erasure models containing a
limited number of erasures per coding window, per sliding window, and
containing erasure bursts of a limited length.Comment: Extended version of a conference paper in the IEEE International
Symposium on Information Theory (ISIT), July 2012. 12 pages, 3 figure
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
Optimal Multiplexed Erasure Codes for Streaming Messages with Different Decoding Delays
This paper considers multiplexing two sequences of messages with two
different decoding delays over a packet erasure channel. In each time slot, the
source constructs a packet based on the current and previous messages and
transmits the packet, which may be erased when the packet travels from the
source to the destination. The destination must perfectly recover every source
message in the first sequence subject to a decoding delay and
every source message in the second sequence subject to a shorter decoding delay
. We assume that the channel loss model
introduces a burst erasure of a fixed length on the discrete timeline.
Under this channel loss assumption, the capacity region for the case where
was previously solved. In this paper, we fully
characterize the capacity region for the remaining case . The key step in the achievability proof is achieving the
non-trivial corner point of the capacity region through using a multiplexed
streaming code constructed by superimposing two single-stream codes. The main
idea in the converse proof is obtaining a genie-aided bound when the channel is
subject to a periodic erasure pattern where each period consists of a
length- burst erasure followed by a length- noiseless
duration.Comment: 20 pages, 1 figure, 1 table, presented in part at 2019 IEEE ISI
Subset Adaptive Relaying for Streaming Erasure Codes
This paper investigates adaptive streaming codes over a three-node relayed
network. In this setting, a source transmits a sequence of message packets
through a relay under a delay constraint of time slots per packet. The
source-to-relay and relay-to-destination links are unreliable and introduce a
maximum of and packet erasures respectively. Recent work has
proposed adaptive (time variant) and nonadaptive (time invariant) code
constructions for this setting and has shown that adaptive codes can achieve
higher rates. However, the adaptive construction deals with many possibilities,
leading to an impractical code with very large block lengths. In this work, we
propose a simplified adaptive code construction which greatly improves the
practicality of the code, with only a small cost to the achievable rates. We
analyze the construction in terms of the achievable rates and field size
requirements, and perform numerical simulations over statistical channels to
estimate packet loss probabilities
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