On the capacity of wireless 1-hop intersession network coding — a broadcast packet erasure channel approach

Motivated by practical wireless network protocols, this paper answers the following questions: Exactly (or at most) how much throughput improvement one can expect from intersession network coding (INC) in a 1-hop neighborhood over non-coding solutions; and how to achieve (or approach) the capacity. Focusing on a two-stage setting, this work first provides a capacity outer bound for any number of M coexisting unicast sessions and any overhearing events modeled by broadcast packet erasure channels that are time-wise independently and identically distributed. For M ≤ 3, it is shown that the outer bound meets the capacity. To quantify the tightness of the outer bound for M ≥ 4, a capacity inner bound for general M is provided. Both bounds can be computed by a linear programming solver. Numeric results show that for 4 ≤ M ≤ 5 with randomly chosen channel parameters, the difference between the outer and inner bounds is within 1% for 99.4% of the times. The results in this paper can also be viewed as the generalization of index-coding capacity from wireline broadcast with binary alphabets to wireless broadcast with high-order alphabets.