1 A New Achievable Rate For A Stochastic Two Relay Network With No Interference Ghosheh Abed Hodtani and Mohammad Reza Aref Department of Electrical Engineering, Sharif University of Technology, Tehran, Iran hodtani@yahoo.com , aref@sharif.edu EXTENDED SUMMARY I. INTRODUCTION Recently there has been much interest in studying relay networks and wireless relay communication scenarios [1], [2].Wireless networks with base stations (cell networks) are relatively well understood by considering the multiple access and the broadcast channels. However, the networks without base stations ( adhoc networks) in which any node can act both as a terminal and as a relay for other transmissions are less well understood and have many open problems. Adhoc networks was studied in [3],[4] as networks having n nodes communicating with each other and multiple source-destination pairs to obtain an achievable rate region using point to point coding. Later, in [5] mobile adhoc networks have been studied. In [6], adhoc networks with one randomly selected source-destination pair was named as relay networks. Also, in [6] arbitrary network coding was suggested to increase the overall efficiency and was used to obtain achievable rates and to derive upper bounds from max-flow min-cut theorem. Here we consider the relay network introduced in [6] with two relays and no interference to obtain a new achievable rate using a new network coding (decode-and-broadcast). In other words, we investigate the two-level relay channel studied in [4,Fig.1] using a new network coding instead of point to point coding. At first, in this section we recall some definitions, define the network model considered, describe the network coding. A. Some definitions Relay network [6] : A relay network is a wireless network having one source-destination pair and some relays where the relays act as terminals (transmitters and receivers). Stochastic (deterministic) relay network with no interference [7],[8] : Stochastic (deterministic) relay network with no interference is a network where the output of every link is some stochastic (deterministic) function of only the input of that link. So, a stochastic (deterministic) relay network with no interference is a special case of relay network introduced in [6]. Deterministic relay networks introduced in [7] have been named as Aref networks in [8]. Remarks : 1. The assumption of no interference is applicable only for broadcast channels and does not apply to multiple access channels and hence to Z-channels. For this reason, we will use decode-and-broadcast coding ( namely, the source and the relays act as broadcast channels). 2. In [9],[10], the relay networks have been studied with a more general definition of determinism ( approximately Gaussian determinism). 3. In deterministic wired network with independent channels [11], we don’t have broadcasting while in a stochastic (deterministic) relay network with no interference and in other wireless networks such as wireless erasure networks [12] we have broadcasting. B. Network model : Here we consider a stochastic two relay network with no interference (Fig.1) consisting of one source (x 0 ), one destination (y 3 ), two relays (x 1 and x 2 ) and seven links: the link between the source and the destination (y 03 ), two links between the relays ( ݕ ଵଶ , ݕ ଶଵ ), two links between the source and the relays ( ݕ ଴ଵ ݕ, ଴ଶ ) and two links between the relays and the destination ( ݕ ଵଷ ݕ, ଶଷ ). Fig.2 illustrates the network model where the message ݓis sent and ultimately ݓෝ is estimated at the receiver. C. The network coding (decode-and-broadcast) : Here we apply a new technique (decode-and-broadcast) established from the combination of superposition encoding [13]-[18] and random binning [18]-[21]. This technique is a generalization of the coding scheme used in This work was supported in part by Iran National Science Foundation.