Optimal Streaming Erasure Codes Over the Three-Node Relay Network

• Published in: IEEE transactions on information theory Vol. 66; no. 5; pp. 2696 - 2712
• 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 01.05.2020; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Cloud computing; Data centers; Delays; Encoding; Forward error correction; maximum achievable rate; message-wise decode-forward; Messages; packet erasures; Relay; Relay networks (telecommunications); Service introduction; streaming; Streaming media; symbol-wise decode-forward; Symbols; three-node relay network
• ISSN: 0018-9448; 1557-9654
• DOI: 10.1109/TIT.2019.2940833

This paper investigates low-latency streaming codes for a three-node relay network. The source transmits a sequence of messages (streaming messages) to the destination through the relay between them, where the first-hop channel from the source to the relay and the second-hop channel from the relay to the destination are subject to packet erasures. Every source message generated at a time slot must be recovered perfectly at the destination within the subsequent T time slots. In any sliding window of <inline-formula> <tex-math notation="LaTeX"> {T}+1 </tex-math></inline-formula> time slots, we assume no more than <inline-formula> <tex-math notation="LaTeX"> {N}_{1} </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">{N}_{2} </tex-math></inline-formula> erasures are introduced by the first-hop channel and second-hop channel respectively. We fully characterize the maximum achievable rate in terms of T , <inline-formula> <tex-math notation="LaTeX"> {N}_{1} </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX"> {N}_{2} </tex-math></inline-formula>. The achievability is proved by using a symbol-wise decode-forward strategy where the source symbols within the same message are decoded by the relay with different delays. The converse is proved by analyzing the maximum achievable rate for each channel when the erasures in the other channel are consecutive (bursty). In addition, we show that traditional message-wise decode-forward strategies, which require the source symbols within the same message to be decoded by the relay with the same delay, are sub-optimal in general.