On the Capacity of Wireless 1-Hop Intersession Network Coding-A Broadcast Packet Erasure Channel Approach

Motivated by practical wireless network protocols, this paper focuses on wireless intersession network coding (INC) over a 1-hop neighborhood, of which the exact capacity region remains an open problem. Towards better understanding of the capacity, this work first models the wireless overhearing events by broadcast packet erasure channels that are memoryless and stationary. Since most INC gain is resulted from destinations overhearing packets transmitted by other sources, this work then focuses exclusively on the 2-staged INC schemes, which fully capture the throughput benefits of overheard message side information (MSI) through the use of one-time feedback but refrain from exploiting the broadcast spatial diversity gain of channel output feedback. Under this setting, a capacity outer bound is provided for any number of coexisting unicast sessions. For the special cases of M <= 3, it is shown that the outer bound can be achieved and is indeed the capacity. To quantify the tightness of the outer bound for M >= 4, a capacity inner bound for general M is provided. Both the outer and inner bounds can be evaluated by any 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 96.7% of the times. Focusing exclusively on the benefits of MSI, 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.