Streaming Erasure Codes over Multi-hop Relay Network

TL;DR

This paper investigates low-latency streaming erasure codes over multi-hop relay networks, proposing a state-dependent coding scheme that approaches the capacity limit more closely than previous state-independent methods.

Contribution

It introduces a novel state-dependent coding scheme for multi-hop relay networks that nearly achieves the theoretical capacity, improving upon existing state-independent strategies.

Findings

State-dependent scheme achieves the upper bound up to header size.

Header size does not depend on field size, reducing the gap as field size increases.

The scheme extends capacity results from three-node to multi-hop networks.

Abstract

This paper studies low-latency streaming codes for the multi-hop network. The source is transmitting a sequence of messages (streaming messages) to a destination through a chain of relays where each hop is subject to packet erasures. Every source message has to be recovered perfectly at the destination within 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 hop channel. The capacity in case of a single relay (a three-node network) was derived by Fong [1], et al. While the converse derived for the three-node case can be extended to any number of nodes using a similar technique (analyzing the case where erasures on other links are consecutive), we demonstrate next that the achievable scheme, which suggested a clever symbol-wise decode and forward strategy, can not be straightforwardly extended without a loss in performance. The coding scheme for the three-node network, which was shown to achieve the upper bound, was ``state-independent'' (i.e., it does not depend on specific erasure pattern). While this is a very desirable property, in this paper, we suggest a ``state-dependent'' (i.e., a scheme which depends on specific erasure pattern) and show that it achieves the upper bound up to the size of an additional header. Since, as we show, the size of the header does not depend on the field size, the gap between the achievable rate and the upper bound decreases as the field size increases.