Optimal Streaming Codes for Channels With Burst and Arbitrary Erasures

• Published in: IEEE transactions on information theory Vol. 65; no. 7; pp. 4274 - 4292
• Main Authors: Fong, Silas L., Khisti, Ashish, Li, Baochun, Tan, Wai-Tian, Zhu, Xiaoqing, Apostolopoulos, John
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.07.2019; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Burst and arbitrary erasures; channel capacity; Channel models; column distance; column span; Convolutional codes; Decoding; Delay; Delays; Forward error correction; Internet; low-latency; Messages; packet erasure channel; Servers; sliding window; streaming codes
• ISSN: 0018-9448; 1557-9654
• DOI: 10.1109/TIT.2019.2894124

This paper considers transmitting a sequence of messages (streaming messages) 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.