Fundamental limits on the suppression of molecular fluctuations.

Negative feedback is common in biological processes and can increase a system's stability to internal and external perturbations. But at the molecular level, control loops always involve signalling steps with finite rates for random births and deaths of individual molecules. Here we show, by developing mathematical tools that merge control and information theory with physical chemistry, that seemingly mild constraints on these rates place severe limits on the ability to suppress molecular fluctuations. Specifically, the minimum standard deviation in abundances decreases with the quartic root of the number of signalling events, making it extremely expensive to increase accuracy. Our results are formulated in terms of experimental observables, and existing data show that cells use brute force when noise suppression is essential; for example, regulatory genes are transcribed tens of thousands of times per cell cycle. The theory challenges conventional beliefs about biochemical accuracy and presents an approach to the rigorous analysis of poorly characterized biological systems.

Gaussian fading is the worst fading

The capacity of peak-power limited, single-antenna, noncoherent, flat-fading channels with memory is considered. The emphasis is on the capacity pre-log, i.e., on the limiting ratio of channel capacity to the logarithm of the signal-to-noise ratio (SNR), as the SNR tends to infinity. It is shown that, among all stationary and ergodic fading processes of a given spectral distribution function and whose law has no mass point at zero, the Gaussian process gives rise to the smallest pre-log. The assumption that the law of the fading process has no mass point at zero is essential in the sense that there exist stationary and ergodic fading processes whose law has a mass point at zero and that give rise to a smaller pre-log than the Gaussian process of equal spectral distribution function. An extension of these results to multiple-input single-output (MISO) fading channels with memory is also presented. © 2006 IEEE.

Channels that heat up

This paper considers an additive noise channel where the time-κ noise variance is a weighted sum of the squared magnitudes of the previous channel inputs plus a constant. This channel model accounts for the dependence of the intrinsic thermal noise on the data due to the heat dissipation associated with the transmission of data in electronic circuits: the data determine the transmitted signal, which in turn heats up the circuit and thus influences the power of the thermal noise. The capacity of this channel (both with and without feedback) is studied at low transmit powers and at high transmit powers. At low transmit powers, the slope of the capacity-versus-power curve at zero is computed and it is shown that the heating-up effect is beneficial. At high transmit powers, conditions are determined under which the capacity is bounded, i.e., under which the capacity does not grow to infinity as the allowed average power tends to infinity. © 2009 IEEE.

Outage exponents of block-fading channels with power allocation

Power allocation is studied for fixed-rate transmission over block-fading channels with arbitrary continuous fading distributions and perfect transmitter and receiver channel state information. Both short- and long-term power constraints for arbitrary input distributions are considered. Optimal power allocation schemes are shown to be direct applications of previous results in the literature. It is shown that the short- and long-term outage exponents for arbitrary input distributions are related through a simple formula. The formula is useful to predict when the delay-limited capacity is positive. Furthermore, this characterization is useful for the design of efficient coding schemes for this relevant channel model. © 2010 IEEE.