Rate-Optimal Streaming Codes Over the Three-Node Decode-And-Forward Relay Network

TL;DR

This paper derives the capacity bounds and constructs rate-optimal streaming codes for a three-node decode-and-forward relay network with delay constraints, under a packet erasure model approximating Gilbert-Elliot channels.

Contribution

It provides the first capacity characterization and explicit code constructions for delay-constrained streaming over relay networks with burst and random erasures.

Findings

Capacity bounds are derived for the relay network under the DCSW erasure model.

Explicit streaming codes are constructed that achieve the capacity bounds.

The codes have linear field size and decoding complexity similar to MDS codes.

Abstract

In this paper, we study the three-node Decode-and-Forward (D&F) relay network subject to random and burst packet erasures. The source wishes to transmit an infinite stream of packets to the destination via the relay. The three-node D&F relay network is constrained by a decoding delay of T packets, i.e., the packet transmitted by the source at time i must be decoded by the destination by time i+T. For the individual channels from source to relay and relay to destination, we assume a delay-constrained sliding-window (DCSW) based packet-erasure model that can be viewed as a tractable approximation to the commonly-accepted Gilbert-Elliot channel model. Under the model, any time-window of width w contains either up to a random erasure or else erasure burst of length at most b (>= a). Thus the source-relay and relay-destination channels are modeled as (a_1, b_1, w_1, T_1) and (a_2, b_2, w_2, T_2) DCSW channels. We first derive an upper bound on the capacity of the three-node D&F relay network. We then show that the upper bound is tight for the parameter regime: max{b_1, b_2}|(T-b_1-b_2-max{a_1, a_2}+1), a1=a2 OR b1=b2 by constructing streaming codes achieving the bound. The code construction requires field size linear in T, and has decoding complexity equivalent to that of decoding an MDS code.