As the size,the cost and the power consumption of communication devices and integrated circuits de- creases designing a system of autonomous sensors,that can monitor the environment and are capable of transporting and processing the information in any point of the controlled area,becomes a concrete goal.While the fabrication technology is mature to make intelligent sensors with wireless communication interfaces which are small and inexpensive,the main challenge in the design of these networks is at the system level. The scenario analyzed in [4 ]is radically di .erent from large networks such as the telephone network that have highly hierarchical architectures:in [4 ]all the nodes have identical function- alities,equal transmission bandwidth and are uniformly distributed over a circular region of .xed radius.
However,[4 ]is neglecting one fundamental aspect of the problem:the nodes samples will be increas- ingly dependent as the density of the nodes increases [7 ].This observation was used in [8 ]where it was proven that distributed codes,that compress separately the correlated samples in each node,can reduce the amount of bits per node per square meter to an O (N .1 ),i.e.much faster than the transport capacity. The limitation of the approach in [8 ]is the high complexity required to have signi .cant compression gain without sharing one single bit of data among the nodes Fortunately,there is no need to impose such constraint.After all,the trademark of multi-hop networks is that power e .cient transmission is achieved when the data travel through several intermediate close-by nodes before reaching their .nal destination. If neighboring nodes were jointly compressing the data before forwarding them remotely,they could save many bits per sample while transmitting with the same or even greater precision.A good engineering design is compelled to exploit this fortunate coincidence by combining routing and and classical (not dis- tributed)source coding.This is the truly novel aspect of our project and,to the best of our knowledge, this connection has not been studied before.