Optimal Streaming Codes for Channels with Burst and Arbitrary Erasures

TL;DR

This paper develops optimal streaming codes for channels experiencing burst and arbitrary erasures, achieving maximum transmission rates while ensuring timely message recovery, and demonstrates their superiority over existing codes in certain channel models.

Contribution

The paper fully characterizes the maximum achievable rate for streaming over channels with burst and arbitrary erasures and constructs optimal codes that attain this rate.

Findings

Optimal streaming codes outperform existing codes in Gilbert-Elliott and Fritchman channels.

Complete characterization of maximum achievable rate for channels with burst and arbitrary erasures.

Construction of codes that achieve the optimal rate and decoding delay constraints.

Abstract

This paper considers transmitting a sequence of messages (a streaming source) over a packet erasure channel. In each time slot, the source constructs a packet based on the current and the previous messages and transmits the packet, which may be erased when the packet travels from the source to the destination. Every source message must be recovered perfectly at the destination subject to a fixed decoding delay. We assume that the channel loss model introduces either one burst erasure or multiple arbitrary erasures in any fixed-sized sliding window. Under this channel loss assumption, we fully characterize the maximum achievable rate by constructing streaming codes that achieve the optimal rate. In addition, our construction of optimal streaming codes implies the full characterization of the maximum achievable rate for convolutional codes with any given column distance, column span and decoding delay. Numerical results demonstrate that the optimal streaming codes outperform existing streaming codes of comparable complexity over some instances of the Gilbert-Elliott channel and the Fritchman channel.