One pervasive challenge in providing a high quality-of-service for live communication is to recover lost packets in real-time. Streaming codes are a class of erasure codes that are designed for such strict, low-latency streaming communication settings. Motivated by applications that transmit messages whose sizes vary over time, such as live video streaming, this paper considers the setting of streaming codes under variable-size messages. In practice, streaming codes operate in an "online" setting where the sizes of the future messages are unknown. "Offline" codes, in contrast, have access to the sizes of all messages, including future ones. This paper introduces the first online rate-optimal streaming codes for communicating over a burst-only packet loss channel for two broad parameter regimes. These two online codes match the rates of optimal offline codes for the two settings despite the apparent advantage of the offline setting. This paper further establishes that online codes cannot attain the optimal rate for offline codes for all remaining parameter settings.

翻译：实时通信中提供高质量服务的一个普遍挑战是即时恢复丢失的数据包。流编码是一类为这种严格、低延迟流式通信场景设计的纠删码。受实时视频流传输等应用中消息大小随时间变化的启发，本文研究了变长消息场景下的流编码问题。实践中，流编码运行于未来消息大小未知的"在线"环境，而"离线"编码则可获知包括未来消息在内的所有消息大小。针对突发丢包信道，本文首次提出两种广泛参数范围内的在线码率最优流编码方案。尽管离线场景具有明显优势，这两种在线编码在两个场景下均能达到最优离线编码的码率。本文进一步证明，在其余所有参数设定下，在线编码无法达到离线编码的最优码率。