Metabolically efficient information processing

Energy-efficient information transmission may be relevant to biological sen sory signal processing as well as to low-power electronic devices. We explo re its consequences in two different regimes. In an "immediate" regime, we argue that the information rate should be maximized subject to a power cons traint, and in an "exploratory" regime, the transmission rate per power cos t should be maximized, in the absence of noise, discrete inputs are optimal ly encoded into Boltzmann distributed output symbols. In the exploratory re gime, the partition function of this distribution is numerically equal to 1 . The structure of the optimal code is strongly affected by noise in the tr ansmission channel. The Arimoto-Blahut algorithm, generalized for cost cons traints, can be used to derive and interpret the distribution of symbols fo r optimal energy-efficient coding in the presence of noise. We outline the possibilities and problems in extending our results to information coding a nd transmission in neurobiological systems.