  This article presents the formulation and steady-state analysis of the
distributed estimation algorithms based on the diffusion cooperation scheme in
the presence of errors due to the unreliable data transfer among nodes. In
particular, we highlight the impact of transmission errors on the least-mean
squares (LMS) adaptive networks. We develop the closed-form expressions of the
steady-state mean-square deviation (MSD) which is helpful to assess the effects
of the imperfect information flow on on the behavior of the diffusion LMS
algorithm in terms of the steady-state error. The model is then validated by
performing Monte Carlo simulations. It is shown that local and global MSD
curves are not necessarily monotonic increasing functions of the error
probability. We also assess sufficient conditions that ensure mean and
mean-square stability of diffusion LMS strategies in the presence of
transmission errors. Moreover, issues such as scalability in the sense of
network size and regressor size, spatially correlated observations, as well as
the effect of the distribution of the noise variance are studied.
  While the proposed theoretical framework is general in the sense that it is
not confined to a particular source of error during information diffusion, for
practical reasons we additionally study a specific scenario where errors occur
at the medium access control (MAC) level. We develop a model to quantify the
MAC-level transmission errors according to the network topology and system
parameters for a set of nodes employing a backoff procedure to access the
channel. To overcome the problem of unreliable data exchange, we propose an
enhanced combining rule that can be deployed in order to improve the
performance of diffusion estimation algorithms by using the knowledge of the
properties of the transmission errors.
