Symbol Detection with Network Coding in Wireless Channels

For multi-sources transmitting to a common sink with assistance of relays where network coding is used, different symbols may experience different fading and noise levels, and there is a need to calculate the average symbol detection error probability at the receiver. In this letter, we present a method that closely bounds the error performance when log-likelihood ratio (LLR) detection is used. The method integrates two techniques including the union bound based on the bit-level input-output weight enumerate function (IOWEF) in coding and the maximum ratio combining (MRC) in diversity analysis. The method is applicable to any network coding matrix used at relay.