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.

翻译：在本文中, 我们研究以随机和爆裂的封包消除为条件的三节解码和前置( D&F) 中继网络 。 源希望通过中继向目的地传输无限的包流。 三节D & F 中继网络受到T包解码延迟的限制, 即源在时间i 上传输的包必须由目的地在时间 +T 上解码。 从源到中继和中继到目的地的单个频道, 我们假设一个基于延迟限制的滚动窗口( DCS) 的包- 范围模式, 可以通过中继向普通接受的 Gilbert- Elliot 频道模式传递无限的包流。 在模式下, 宽度的任何时间- 窗口都包含随机的破译或其它时间的缩缩略时间 i+T+T 。 因此, 源- 和中继和中继的频道以 (a_ 1, b_ 1, w_ 1, T_ 1) 和 (a_ 2, b_ 2, t_ 2, T_ 等等等 等的 等 级系统显示我们第一个捆绑定的 Serview. b 的系统 的系统系统系统显示的系统显示的上显示 a a a a- b_ b_ b_ b_ b_ AS AS 的系统显示 a AS 的高级系统显示的系统显示 a stral sal sal str str stral sal stral 的系统 的系统 的系统 的系统 的系统 的系统的系统的系统 的 。