Bounds on Decoding Failure Probability in Linear Network Coding Schemes with Erasure Channels

We consider a performance analysis for decoding the source information in linear network coding schemes with erasure channels. Multiple relays assist in the successful transmission of source messages to their destination. Owing to unreliable communication links, network connections between nodes vary, leading to a failure of relays for generating the linear combinations of incoming messages in network coding scenarios. In this letter, we derive upper and lower bounds on the decoding failure probability in which a network code matrix does not have full rank in the dynamic network connections. We then investigate the impact of the major parameters, i.e., the number of relays, a finite field size, and the erasure probability, on the decoding performance.