Layered Constructions for Low-Delay Streaming Codes

We study error correction codes for multimedia streaming applications where a stream of source packets must be transmitted in real-time, with in-order decoding, and strict delay constraints. In our setup, the encoder observes a stream of source packets in a sequential fashion, and <inline-formula> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula> channel packets must be transmitted between the arrival of successive source packets. Each channel packet can depend on all the source packets observed up to and including that time, but not on any future source packets. The decoder must reconstruct the source stream with a delay of <inline-formula> <tex-math notation="LaTeX">$T$ </tex-math></inline-formula> packets. We consider a class of packet erasure channels with burst and isolated erasures, where the erasure patterns are locally constrained. Our proposed model provides a tractable approximation to statistical models, such as the Gilbert–Elliott channel, for capacity analysis. When <inline-formula> <tex-math notation="LaTeX">$M=1$ </tex-math></inline-formula>, i.e., when the source-packet arrival and channel-packet transmission rates are equal, we establish upper and lower bounds on the capacity, that are within one unit of the decoding delay <inline-formula> <tex-math notation="LaTeX">$T$ </tex-math></inline-formula>. We also establish necessary and sufficient conditions on the column distance and column span of a convolutional code to be feasible, and in turn establish a fundamental tradeoff between these. Our proposed codes—maximum distance and span codes—achieve a near-optimal tradeoff between the column distance and column span, and involve a layered construction. When <inline-formula> <tex-math notation="LaTeX">$M>1$ </tex-math></inline-formula>, we establish the capacity for the burst-erasure channel and an achievable rate in the general case. Extensive numerical simulations over Gilbert–Elliott and Fritchman channel models suggest that our codes also achieve significant gains in the residual loss probability over statistical channel models.