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 contributions are, 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 2m, where m is a positive integer. To reduce computational complexity, a subgraph decomposition approach is proposed. In general, it can significantly reduce 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 results in low BEP regions with much lower complexity.