Consider a noisy linear observation model with an unknown permutation, based on observing $y = \Pi ^{*} A x^{*} + w$ , where $x^{*} \in {\mathbb {R}} ^{d}$ is an unknown vector, $\Pi ^{*}$ is an unknown $n \times n$ permutation matrix, and $w \in {\mathbb {R}} ^{n}$ is additive Gaussian noise. We analyze the problem of permutation recovery in a random design setting in which the entries of matrix $A$ are drawn independently from a standard Gaussian distribution and establish sharp conditions on the signal-to-noise ratio, sample size $n$ , and dimension $d$ under which $\Pi ^{*}$ is exactly and approximately recoverable. On the computational front, we show that the maximum likelihood estimate of $\Pi ^{*}$ is NP-hard to compute for general $d$ , while also providing a polynomial time algorithm when $d =1$ .

Linear Regression With Shuffled Data: Statistical and Computational Limits of Permutation Recovery

The design of biologically-inspired wireless communication systems using bacteria as the basic element of the system is initially motivated by a phenomenon called Quorum Sensing. Due to high randomness in the individual behavior of a bacterium, reliable communication between two bacteria is almost impossible. Therefore, we have recently proposed that a population of bacteria in a cluster is considered as a bio node in the network capable of molecular transmission and reception. This proposition enables us to form a reliable bio node out of many unreliable bacteria. In this paper, we study the communication between two nodes in such a network where information is encoded in the concentration of molecules by the transmitter. The molecules produced by the bacteria in the transmitter node propagate through the diffusion channel. Then, the concentration of molecules is sensed by the bacteria population in the receiver node which would decode the information and output light or fluorescent as a result. The uncertainty in the communication is caused by all three components of communication, i.e., transmission, propagation and reception. We study the theoretical limits of the information transfer rate in the presence of such uncertainties. Finally, we consider M-ary signaling schemes and study their achievable rates and corresponding error probabilities.

Design and Analysis of Wireless Communication Systems Using Diffusion-Based Molecular Communication Among Bacteria

In this paper, we study the recovery of a signal from a set of noisy linear projections (measurements), when such projections are unlabeled, that is, the correspondence between the measurements and the set of projection vectors (i.e., the rows of the measurement matrix) is not known a priori . We consider a special case of unlabeled sensing referred to as unlabeled ordered sampling (UOS) where the ordering of the measurements is preserved. We identify a natural duality between this problem and classical compressed sensing (CS), where we show that the unknown support (location of nonzero elements) of a sparse signal in CS corresponds to the unknown indices of the measurements in UOS. While in CS, it is possible to recover a sparse signal from an underdetermined set of linear equations (less equations than the signal dimension), successful recovery in UOS requires taking more samples than the dimension of the signal. Motivated by this duality, we develop a restricted isometry property (RIP) similar to that in CS. We also design a low-complexity alternating minimization algorithm that achieves a stable signal recovery under the established RIP. We analyze our proposed algorithm for different signal dimensions and number of measurements theoretically and investigate its performance empirically via numerical simulations. The results are reminiscent of a phase transition occurring in CS.

Signal Recovery From Unlabeled Samples

We provide a fundamental treatment of the molecular communication channel wherein “inscribed matter” is transmitted across a spatial gap to provide reliable signaling between a sender and receiver. Inscribed matter is defined as an ensemble of “tokens” (biotic/abiotic objects) and is inspired, at least partially, by biological systems where groups of individually constructed discrete particles ranging from molecules to viruses and organisms are released by a source and travel to a target—for example, morphogens or semiochemicals diffuse from one cell, tissue, or organism to another. For identical-tokens that are neither lost nor modified, we consider messages encoded using three candidate communication schemes: 1) token timing (timed release); 2) token payload (composition); and 3) token timing plus payload. We provide capacity bounds for each scheme and discuss their relative utility. We find that under not unreasonable assumptions, megabit per second rates could be supported at 100 femtoWatt transmitter powers. Since quantities such as token concentration or token counting are derivatives of token arrival timing, token timing undergirds all molecular communication techniques. Thus, our modeling and results about the physics of efficient token-based information transfer can inform investigations of diverse theoretical and practical problems in engineering and biology. This paper, Part I, focuses on the information theoretic bounds on capacity. Part II develops some of the mathematical and information theoretic machinery that support the bounds presented here.

pdf/inscribed-matter-communication-part-ii-4mtdayvbgg.pdf

Inscribed Matter Communication: Part II

The design of biologically-inspired wireless communication systems using bacteria as the basic element of the system is initially motivated by a phenomenon called \emph{Quorum Sensing}. Due to high randomness in the individual behavior of a bacterium, reliable communication between two bacteria is almost impossible. Therefore, we have recently proposed that a population of bacteria in a cluster is considered as a bio node in the network capable of molecular transmission and reception. This proposition enables us to form a reliable bio node out of many unreliable bacteria. 
In this paper, we study the communication between two nodes in such a network where information is encoded in the concentration of molecules by the transmitter. The molecules produced by the bacteria in the transmitter node propagate through the diffusion channel. Then, the concentration of molecules is sensed by the bacteria population in the receiver node which would decode the information and output light or fluorescent as a result. The uncertainty in the communication is caused by all three components of communication, i.e., transmission, propagation and reception. We study the theoretical limits of the information transfer rate in the presence of such uncertainties. Finally, we consider M-ary signaling schemes and study their achievable rates and corresponding error probabilities.

We derive the maximum mutual information for an additive exponential noise (AEN) channel with a peak input constraint. We find that the optimizing input density is mixed (with singularities) similar to previous results for AEN channels with a mean input constraint. Likewise, the maximum mutual information takes a similar form, though obviously the maximum for the peak constraint is smaller than for the corresponding mean-constrained channel. This model is inspired by multiple biological phenomena and processes which can be abstracted as follows: inscribed matter is sent by an emitter, moves through a medium, and arrives eventually at its destination receptor. The inscribed matter can convey information in a variety of ways such as the number of signaling quanta - molecules, macromolecular complexes, organelles, cells and tissues - that are emitted as well as the detailed pattern of their release. However, rather than focus on a general class of emitter-receptor systems or a particular exemplar of biomedical importance, our ultimate goal is to provide bounds on the potential efficacy of timed-release signaling for any system which emits identical signaling quanta. That is, we seek to apply one of the most potent aspects of information theory to biological signaling - mechanism blindness - in the hopes of gaining insights applicable to diverse systems that span a wide range of spatiotemporal scales.

/pdf/an-additive-exponential-noise-channel-with-a-transmission-1nyf4kkbhq.pdf

An additive exponential noise channel with a transmission deadline

We consider mutual information between release times and capture times for a set of M identical quanta traveling independently from a source to a target. The quanta are immediately captured upon arrival, rst-passage times are assumed independent and identically distributed and the quantum emission times are constrained by a deadline. The primary application area is intended to be inter/intracellular molecular signaling in biological systems whereby an organelle, cell or group of cells must deliver some message (such as transcription or developmental instructions) over distance with reasonable certainty to another organelles, cells or group of cells. However, the model can also be applied to communications systems wherein indistinguishable signals have random transit latencies.

Timing Channels with Multiple Identical Quanta

For model predictive current control (MPCC) strategy, it's poor dynamic response caused by speed loop PI control and poor parameter robustness are the main factors restricting its development. So, this paper proposes a model predictive current control based on sliding mode observer with better tracking ability of current and speed under disturbance. First, this paper analyzes the effect of motor parameter mismatches on current predicted values from multiple perspectives. And a sliding mode disturbance observer is designed to compensate lumped disturbances including parameter mismatches and unmodeled dynamic disturbances into prediction model. Then, the speed loop PI controller in model predictive current control is replaced by a deadbeat predictive controller to improve response speed of the speed loop. Meanwhile, the sliding mode load torque observer is constructed to observe the load torque and sends it into the deadbeat predictive controller to improve the anti-load disturbance performance of the control system. Furthermore, a sliding mode reaching law based on sinusoidal saturation function is proposed to suppress chattering of sliding mode observer. The experiments demonstrate that the proposed control strategy not only has faster dynamic response but also has good speed and current tracking performance under lumped disturbance and load disturbance.

Model Predictive Current Control of Permanent Magnet Synchronous Motor Based on Sliding Mode Observer With Enhanced Current and Speed Tracking Ability Under Disturbance

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An additive exponential noise channel with a transmission deadline

Timing Channels with Multiple Identical Quanta

Model Predictive Current Control of Permanent Magnet Synchronous Motor Based on Sliding Mode Observer With Enhanced Current and Speed Tracking Ability Under Disturbance