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This paper studies low-latency streaming codes for the multi-hop network. Thesource is transmitting a sequence of messages (streaming messages) to adestination through a chain of relays where each hop is subject to packeterasures. Every source message has to be recovered perfectly at the destinationwithin a delay constraint of $T$ time slots. In any sliding window of $T+1$time slots, we assume no more than $N_j$ erasures introduced by the $j$'th hopchannel. The capacity in case of a single relay (a three-node network) wasderived by Fong [1], et al. While the converse derived for the three-node casecan be extended to any number of nodes using a similar technique (analyzing thecase where erasures on other links are consecutive), we demonstrate next thatthe achievable scheme, which suggested a clever symbol-wise decode and forwardstrategy, can not be straightforwardly extended without a loss in performance.The coding scheme for the three-node network, which was shown to achieve theupper bound, was ``state-independent'' (i.e., it does not depend on specificerasure pattern). While this is a very desirable property, in this paper, wesuggest a ``state-dependent'' (i.e., a scheme which depends on specific erasurepattern) and show that it achieves the upper bound up to the size of anadditional header. Since, as we show, the size of the header does not depend onthe field size, the gap between the achievable rate and the upper bounddecreases as the field size increases.

Streaming Erasure Codes over Multi-hop Relay Network