On carrier sense multiple access in coded wireless packet networks

We introduce a Markov model for the wireless broadcast advantage in carrier sense multiple access networks. The model uses a channel access Markov chain, which captures medium access and packet transmissions of all nodes, and a packet reception Markov chain, which accounts for successful reception or packet loss jointly at all nodes within range. The packet loss process is modeled as a two stage loss process jointly across all receivers to capture various loss effects-packet length dependent and independent-and the wireless broadcast advantage. We derive the average information value of a broadcast with unslotted random access in networks where random linear network coding is applied. The achievable multicast throughput is characterized by the coding subgraph, for which we determine feasibility conditions and fixed point iteration schemes to obtain suitable medium access parameters. Two special carrier sensing situations, namely Aloha and large sensing ranges, lead to hidden monotonicity and convexity structures in the feasibility conditions, which leads to strong fixed point characterizations.