Outage Probability Analysis of Linear Block Network Coding (LBNC) in Wireless Relay Networks

Considering a wireless relay network composed of a source, several relays and a destination, a linear block network coding (LBNC) scheme is proposed to combat the lossy nature of wireless channel. The relays not only replicate the messages received but also perform network coding according to a linear block generator matrix. A special case of LBNC, parity-check network coding (PCNC) scheme is firstly theoretically analyzed and the explicit Average Outage Probability (AOP) and Block Outage Probability (BOP) are derived. For comparison, advanced relay cooperation (ARC), where relays only replicate and forward messages without coding them, is also presented and analyzed. Numerical results show that PCNC performs better than ARC when SNR is high and the s - r link is in good condition. For general LBNC scheme, it is very complicated to calculate the precise outage probability due to the difference of generator matrices, and we turn to simulation to evaluate the outage performance. The result shows that the performance of (M + C, M) LBNC can be estimated by (left perpendicularM/Cright perpendicular + 1, left perpendicularM/Cright perpendicular) and (inverted right perpendicularM/Cinverted left perpendicular + 1, inverted right perpendicularM/Cinverted left perpendicular) PCNC.