Maximum-Likelihood Decoding and Performance Analysis of a Noisy Channel Network with Network Coding

We investigate sink decoding methods and performance analysis approaches for a network with intermediate node encoding (coded network). The network consists of statistically independent noisy channels. The sink bit error probability (BEP) is the performance measure. We first discuss soft-decision decoding without statistical information on the upstream channels (the channels not directly connected to the sink). The example shows that the decoder cannot significantly improve the BEP from the hard-decision decoder. We develop the union bound to analyze the decoding approach. The bound can show the asymptotic (regarding SNR: signal-to-noise ratio) performance. Using statistical information of the upstream channels, we then show the method of maximum-likelihood (ML) decoding. With the decoder, a significant improvement in the BEP is obtained. To evaluate the union bound for the ML decoder, we use an equivalent signal point procedure. It can be reduced to a least-squares problem with linear constraints for medium-to-high SNR.