Interaction of Coding and Multihop Transmission in Wireless Networks

For multihop wireless networks, a fundamental question is whether it is advantageous to route over many short hops (short-hop routing) or over a smaller number of longer hops (long-hop routing). Short-hop routing has gained a lot of support, and its proponents mainly produce two arguments: higher SNR at every hop and smaller interference. This paper focuses on the first argument and examines different routing strategies from an informationtheoretic perspective, taking into account the rate penalty incurred by multihop transmission. We analytically derive the optimum number of hops for a linear network given the path loss exponent and the desired end-to-end rate for the case where the delay is not constrained. The analysis is based on the concept of asymptotic spectral efficiency. It turns out that routing over longer hops is competitive for higher rates; in particular, single-hop transmission outperforms two-hop transmission if the rate is larger than the path loss exponent. For delay-constrained transmission, we compare single-hop and two-hop transmission using a sphere-packing bound and simulations with practical codes, taking into account the reduced block length in the two-hop case.