Two enablers of the 5th Generation (5G) of mobile communication systems are the high data rates achievable with millimeter-wave radio signals and the cloudification of the network's mobile edge, made possible also by Multi-access Edge Computing (MEC). In 5G networks, user devices may exploit the high capacity of their mobile connection and the computing capabilities of the edge cloud to offload computational tasks to MEC servers, which run applications on devices' behalf. This paper investigates new methods to perform power- and latency-constrained offloading. First, aiming to minimize user devices' transmit power, the opportunity to exploit concurrent communication links between the device and the edge cloud is studied. The optimal number of channels for simultaneous transmission is characterized in a deterministic and a probabilistic scenario. Subsequently, blocking events that obstruct millimeter-wave channels making them `intermittent' are considered. Resource overprovisioning and error-correcting codes against asymmetric block erasures are proposed to jointly contrast blocking and exploit multi-link communications' diversity. The asymmetric block-erasure channel is characterized by a study of its outage probability. The analysis is performed in a framework that yields closed-form expressions. These, together with corroborating numerical results, are intended to provide reference points and bounds to optimal performance in practical applications.