On the Bit Error Probability of Noisy Channel Networks with Intermediate Node Encoding

We investigate the calculation approach of the sink bit error probability (BEP) for a network with intermediate node encoding. The network consists of statistically independent noisy channels. The main contributionsare, for binary network codes, an error marking algorithm is given to collect the error weight (the number of erroneous bits). Thus, we can calculate the exact sink BEP from the channel BEPs. Then we generalize the approach to nonbinary codes. The coding scheme works on the Galois field 2 , where m is a positive integer. To reduce computational complexity, a subgraph decomposition approach is proposed. In general, it can significantlyreduce computational complexity, and the numerical result is also exact. For approximate results, we discuss the approach of only considering error events in a single channel. The results well approximate the exact resultsin low BEP regions with much lower complexity

On the Diversity Order and Coding Gain of Multi-Source Multi-Relay Cooperative Wireless Networks with Binary Network Coding

In this paper, a multi-source multi-relay cooperative wireless network with binary modulation and binary network coding is studied. The system model encompasses: i) a demodulate-and-forward protocol at the relays, where the received packets are forwarded regardless of their reliability; and ii) a maximum-likelihood optimum demodulator at the destination, which accounts for possible demodulations errors at the relays. An asymptotically-tight and closed-form expression of the end-to-end error probability is derived, which clearly showcases diversity order and coding gain of each source. Unlike other papers available in the literature, the proposed framework has three main distinguishable features: i) it is useful for general network topologies and arbitrary binary encoding vectors; ii) it shows how network code and two-hop forwarding protocol affect diversity order and coding gain; and ii) it accounts for realistic fading channels and demodulation errors at the relays. The framework provides three main conclusions: i) each source achieves a diversity order equal to the separation vector of the network code; ii) the coding gain of each source decreases with the number of mixed packets at the relays; and iii) if the destination cannot take into account demodulation errors at the relays, it loses approximately half of the diversity order.Comment: 35 pages, submitted as a Journal Pape