Optimal Decoding and Performance Analysis of a Noisy Channel Network with Network Coding

We investigate sink decoding approaches and performance analysis 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. First, we investigate soft-decision decoding without statistical information on the upstream channels (the channels not directly connected to the sink). Numerical results show that the decoder cannot significantly improve the performance from a hard-decision decoder. We develop union bounds for analysis. The bounds show the asymptotic (regarding SNR: signal-to-noise ratio) performance of the decoder. Using statistical information about the upstream channels, we can find the error patterns of final hop channels (channels directly connected to sinks).With the error patterns, maximum-likelihood (ML) decoding can be performed, and a significant improvement in the BEP is obtained. To evaluate the union bound for the ML decoder, we use an equivalent point procedure. It is reduced to the least-squares problem with a linear constraint in the medium-to-high SNR region. With deterministic knowledge of the errors in the upstream channels, a genie-aided decoder can further improve the performance. We give the union bound for the genie decoder, which is straightforward to evaluate. By analyzing these decoders, we find that knowledge about the upstream channels is essential for good sink decoding.