A Joint Channel-Network Coding Based on Product Codes for the Multiple-Access Relay Channel

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.