Joint Unitary Triangularization for Gaussian Multi-User MIMO Networks

The problem of transmitting a common message to multiple users over the Gaussian multiple-input multiple-output broadcast channel is considered, where each user is equipped with an arbitrary number of antennas. A closed-loop scenario is assumed, for which a practical capacity-approaching scheme is developed. By applying judiciously chosen unitary operations at the transmit and receive nodes, the channel matrices are triangularized so that the resulting matrices have equal diagonals, up to a possible multiplicative scalar factor. This, along with the utilization of successive interference cancellation, reduces the coding and decoding tasks to those of coding and decoding over the single-antenna additive white Gaussian noise channel. Over the resulting effective channel, any off-the-shelf code may be used. For the two-user case, it was recently shown that such joint unitary triangularization is always possible. In this paper, it is shown that for more than two users, it is necessary to carry out the unitary linear processing jointly over multiple channel uses, i.e., space-time processing is employed. It is further shown that exact triangularization, where all resulting diagonals are equal, is still not always possible, and appropriate conditions for the existence of such are established for certain cases. When exact triangularization is not possible, an asymptotic construction is proposed, that achieves the desired property of equal diagonals up to edge effects that can be made arbitrarily small, at the price of processing a sufficiently large number of channel uses together.Comment: Extended version of published paper in IEEE Transactions on Information Theory, vol. 61, no. 5, pp. 2662-2692, May 201

A computationally engineered RAS rheostat reveals RAS-ERK signaling dynamics.

Synthetic protein switches controlled with user-defined inputs are powerful tools for studying and controlling dynamic cellular processes. To date, these approaches have relied primarily on intermolecular regulation. Here we report a computationally guided framework for engineering intramolecular regulation of protein function. We utilize this framework to develop chemically inducible activator of RAS (CIAR), a single-component RAS rheostat that directly activates endogenous RAS in response to a small molecule. Using CIAR, we show that direct RAS activation elicits markedly different RAS-ERK signaling dynamics from growth factor stimulation, and that these dynamics differ among cell types. We also found that the clinically approved RAF inhibitor vemurafenib potently primes cells to respond to direct wild-type RAS activation. These results demonstrate the utility of CIAR for quantitatively interrogating RAS signaling. Finally, we demonstrate the general utility of our approach in design of intramolecularly regulated protein tools by applying it to the Rho family of guanine nucleotide exchange factors

Why Does a Kronecker Model Result in Misleading Capacity Estimates?

Many recent works that study the performance of multi-input multi-output (MIMO) systems in practice assume a Kronecker model where the variances of the channel entries, upon decomposition on to the transmit and the receive eigen-bases, admit a separable form. Measurement campaigns, however, show that the Kronecker model results in poor estimates for capacity. Motivated by these observations, a channel model that does not impose a separable structure has been recently proposed and shown to fit the capacity of measured channels better. In this work, we show that this recently proposed modeling framework can be viewed as a natural consequence of channel decomposition on to its canonical coordinates, the transmit and/or the receive eigen-bases. Using tools from random matrix theory, we then establish the theoretical basis behind the Kronecker mismatch at the low- and the high-SNR extremes: 1) Sparsity of the dominant statistical degrees of freedom (DoF) in the true channel at the low-SNR extreme, and 2) Non-regularity of the sparsity structure (disparities in the distribution of the DoF across the rows and the columns) at the high-SNR extreme.Comment: 39 pages, 5 figures, under review with IEEE Trans. Inform. Theor

Achievable Rates of Concatenated Codes in DNA Storage under Substitution Errors

In this paper, we study achievable rates of concatenated coding schemes over a deoxyribonucleic acid (DNA) storage channel. Our channel model incorporates the main features of DNA-based data storage. First, information is stored on many, short DNA strands. Second, the strands are stored in an unordered fashion inside the storage medium and each strand is replicated many times. Third, the data is accessed in an uncontrollable manner, i.e., random strands are drawn from the medium and received, possibly with errors. As one of our results, we show that there is a significant gap between the channel capacity and the achievable rate of a standard concatenated code in which one strand corresponds to an inner block. This is in fact surprising as for other channels, such as $q$-ary symmetric channels, concatenated codes are known to achieve the capacity. We further propose a modified concatenated coding scheme by combining several strands into one inner block, which allows to narrow the gap and achieve rates that are close to the capacity.Comment: Extended version of a paper submitted to International Symposium on Information Theory and Its Applications (ISITA) 202

Molecular Simulations of Alternate Frame Folding in Engineered Protein-Based Switches

Living organisms take advantage of proteins in order to carry out most of the biological tasks that keep them alive. Although most proteins do not drastically change shape, some behave as conformational switches: in response to an outside signal from its environment, the protein will shape-change to either an “on” or “off” position. These properties of conformational switches have motivated recent efforts towards the conversion of regular ligand binding proteins into novel switches for use as optical sensors and therapeutics. Here we seek to examine one such design that exhibits an intermolecular tug-of-war between two alternate frames of folding that can be made sensitive to calcium. The challenges of elucidating structural and mechanistic details from a partially unfolded protein have led us to consider coarse-grained simulation techniques. We plan to demonstrate that results from these simulations are in agreement with experimental data and can provide novel insight into the mechanisms of switching in this class of engineered proteins