Optimal Streaming Codes for Channels with Burst and Arbitrary Erasures

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 induces either a single burst erasure or multiple arbitrary erasures in all sliding windows of a fixed size. Under this channel loss model assumption, we fully characterize the maximum achievable rate by constructing streaming codes that achieve the optimal rate. In addition, our code construction 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.