On the block error probability of finite-length codes in decentralized wireless networks

The block error probability of large decentralized wireless networks for fixed code length and rate is investigated. The network model consists of a large number of nodes, distributed according to a homogeneous Poisson point process, emitting their messages independently from the others. The transmitted signals are attenuated due to both path loss and fading. First, we show that in the asymptotic regime, when the code length is long enough, and users communicate with Gaussian codebooks, the error probability behaves as the well known outage probability. Here outage events are induced by fading and interference. Second, in the non-asymptotic regime, we bound the block error probability as a function of the code length and the rate. Applications of these results arise in the context of decentralized wireless networks, e.g. mobile ad hoc networks (MANETs).