It is essential to develop energy-efficient communication techniques for nanoscale wireless communications. In this paper, a new modulation and a novel minimum energy coding scheme (MEC) are proposed to achieve energy efficiency in wireless nanosensor networks (WNSNs). Unlike existing studies, MEC maintains the desired code distance to provide reliability, while minimizing energy. It is analytically shown that, with MEC, codewords can be decoded perfectly for large code distances, if the source set cardinality is less than the inverse of the symbol error probability. Performance evaluations show that MEC outperforms popular codes such as Hamming, Reed-Solomon and Golay in the average codeword energy sense.

We consider the problem of identifying the causal direction between two discrete random variables using observational data. Unlike previous work, we keep the most general functional model but make an assumption on the unobserved exogenous variable: Inspired by Occam's razor, we assume that the exogenous variable is simple in the true causal direction. We quantify simplicity using Renyi entropy. Our main result is that, under natural assumptions, if the exogenous variable has low H0 entropy (cardinality) in the true direction, it must have high H0 entropy in the wrong direction. We establish several algorithmic hardness results about estimating the minimum entropy exogenous variable. We show that the problem of finding the exogenous variable with minimum H1 entropy (Shannon Entropy) is equivalent to the problem of finding minimum joint entropy given n marginal distributions, also known as minimum entropy coupling problem. We propose an efficient greedy algorithm for the minimum entropy coupling problem, that for n=2 provably finds a local optimum. This gives a greedy algorithm for finding the exogenous variable with minimum Shannon entropy. Our greedy entropy-based causal inference algorithm has similar performance to the state of the art additive noise models in real datasets. One advantage of our approach is that we make no use of the values of random variables but only their distributions. Our method can therefore be used for causal inference for both ordinal and also categorical data, unlike additive noise models.

Wireless nanosensor networks (WNSNs), which are collections of nanosensors with communication units, can be used for sensing and data collection with extremely high resolution and low power consumption for various applications. In order to realize WNSNs, it is essential to develop energyefficient communication techniques, since nanonodes are severely energy-constrained. In this paper, a novel minimum energy coding scheme (MEC) is proposed to achieve energy-efficiency in WNSNs. Unlike the existing minimum energy codes, MEC maintains the desired Hamming distance, while minimizing energy, in order to provide reliability. It is analytically shown that, with MEC, codewords can be decoded perfectly for large code distance, if source set cardinality, M is less than inverse of symbol error probability, 1/ps. Performance analysis shows that MEC outperforms popular codes such as Hamming, Reed-Solomon and Golay in average energy per codeword sense.

Recently, ICT community has focused on developing methods to reduce energy dissipation. Although there are numerous attempts to reduce the energy dissipation of communication and computing systems in-use today, the effort to achieve fundamental energy limits for these systems is fade. In this article, we reveal the existing studies on fundamental communication and computing limits, and possible research directions. Moreover, we indicate the substantial role of ICT on carbon reduction, rather than energy. Lastly, we present efforts to find the minimum energy consumption in networks and open issues in a layered internet architecture with fundamental energy consumption per information bit.

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