1 Abstract—Broadcast of a message to nodes in a network is one of elementary but inevitable techniques in wireless ad-hoc and sensor networks. In this paper, we apply the protocol, which the authors proposed for cooperative multi-hop relay networks, to message broadcast over random error channels. Performance is evaluated in terms of the delivery ratio by means of computer simulations. The proposed protocol utilizes an MDS code and a relay node randomly transfers one of partitioned codeword blocks rather than the original message. We suppose a network of square-lattice topology as a preliminary example. Numerical results show that the significant performance improvement can be achieved, in particular, if a relay node can make use of previously received erroneous codeword blocks in the decoding procedure of the MDS code. Index Terms—Broadcast, communications, Delivery ratio, MDS codes, Random error channels I. INTRODUCTION ESSAGE broadcast is a common scenario in wireless ad-hoc and sensor networks. For example, in the AODV (Ad-hoc On-demand Distance Vector) routing protocol, RREQ (Route-Request) messages should be properly broadcast in order to find a route to the destination [1]. When we deliver a message to all the nodes in a network, ``flooding'' is the most simple and basic mechanism [2]. In the flooding mechanism, every relay node transfers the message, upon its first reception, to nodes within its transmission range. Performance of the flooding mechanism has been investigated, for example, from the viewpoint of the connectivity among nodes in conjunction with the percolation theory [3]–[6]. In [3], the probability of survivability of the flooding is discussed. In [4], the forwarding Manuscript received December 10, 2012. Shuji Kobayashi is with the Department of Information and Communication Engineering, Faculty of Computer Science and System Engineering, Okayama Prefectural University, Soja, 719-1197 Japan. (e-mail: s-koba@c.oka-pu.ac.jp). Katsumi Sakakibara is with the Department of Information and Communication Engineering, Faculty of Computer Science and System Engineering, Okayama Prefectural University, Soja, 719-1197 Japan. (phone: +81-866-94-2109; Fax: +81-866-94-2199; e-mail: sakaki@c.oka-pu.ac.jp). Jumpei Taketsugu is with the Department of Information and Communication Engineering, Faculty of Computer Science and System Engineering, Okayama Prefectural University, Soja, 719-1197 Japan. (e-mail: taketugu@c.oka-pu.ac.jp). probability at a node in the flooding is evaluated on the assumption that every node knows the number of its own neighboring nodes. Raman and Gupta investigated performance tradeoffs in terms of latency and energy consumption in percolation-based broadcast protocols [5]. In [6], the authors established the conditions for full connectivity in a network graph, based on the results obtained from bond percolation in a two-dimensional lattice. In wireless ad-hoc networks employing the flooding, it is usual that a message can reach to a relay node through one or more routes. In such a case, multi-route diversity can favorably achieve performance improvement by means of cooperative transmission techniques [7]. The probability of successful broadcast at a relay node which receives two or more copies of the message to be transferred can be improved, since it suffices for a relay node to receive at least one copy correctly. For a cooperative multi-hop networks over random error channels, the authors have proposed the use of MDS (Maximum Distance Separable) codes [8]. In the proposed scheme, the message to be forwarded is encoded at a relay node by an MDS code of coding rate 1/ L , where L is a positive integer. Then, a codeword is partitioned into L blocks and one of the L blocks is forwarded to neighboring nodes rather than the original message. At a receiving node, received codeword blocks are aggregated and then decoded with the MDS decoder. Assuming a simple tandem cooperative topology, the authors theoretically analyzed the performance of the proposed scheme in terms of the outage probability by means of a non-homogeneous absorbing Markov chain [8]. In this paper, we apply the protocol proposed in [8] to the flooding mechanism over a network with square-lattice topology and evaluate the delivery ratio by exhaustive computer simulations. It can happen that a relay node which failed in retrieving the message can receive other codeword blocks some other time. Therefore, in applying the protocol, we can suppose two decoding procedures of the MDS code employed at a relay node. One procedure is that a relay node discards received blocks if it fails to retrieve the message, whereas the other procedure is that a relay node stores the erroneous blocks in its memory for the sake of decoding invoked afterward. The rest of the present paper is organized as follows: Section Message Broadcast Using Random Relaying of Partitioned MDS Codeword Blocks over Random Error Channels Shuji Kobayashi, Katsumi Sakakibara, and Jumpei Taketsugu M Cyber Journals: Multidisciplinary Journals in Science and Technology, Journal of Selected Areas in Telecommunications (JSAT), December Edition, 2012