The multiple access relay channel with network coding has the potential to achieve diversity and improve coverage of wireless networks. Its network coding scheme provides an extra redundancy that can be used at the receiver to improve the performance of the cooperating users. This paper shows that the combination of channel coding and network coding, in the multiple access relay channel, can be seen as a product code with rows formed by the code-words of the individual channel codes of the users and columns formed by the network coding code-words. This new representation allows the use of any decoding algorithm of product codes at the receiver to decode the information data of the cooperating users. This decoding process is a complete joint channel-network decoding algorithm as it sees the combination of the two coding schemes as a single coding scheme. It also gives the possibility to use network coding schemes more powerful than conventional XOR-based network coding. The obtained results show that the proposed product-based network coding structure can improve the performance of the multiple-access relay channel without reducing its efficiency and allow a very flexible cooperation between the involved users. 1. Introduction Cooperative communication [1–4] via relay nodes in cellular networks is an efficient and inexpensive way to achieve spatial diversity gain. Relay nodes deployed in the network can act as a cooperating node by listening to the transmissions performed by different nodes and forwarding them towards the destination. The throughput of cellular networks can be improved further by allowing relay nodes to forward linear combinations, based on network coding [5], of received packets instead of forwarding each packet separately. A well-known scheme that employs cooperation via a fixed relay node is the multiple-access relay channel (MARC) which could be used for the cooperation of two mobile users to a base station with the help of a relay node. Several research work in the literature has shown that network coding in cellular relaying systems provides the same diversity gain as that of conventional two-hop relay channels while improving the system throughput by a factor of 4/3 [6–13]. However, most of these studies were based on computing the outage probability without considering the interaction between channel and network coding. In fact, a relay cannot only be used to gain diversity, its transmission can be seen as an extra redundancy at the receiver, which gives the possibility to improve the link performance as compared to
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