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1. Online variable-length source coding for minimum bitrate LQG control

   Cuvelier, T. C.; Tanaka, T.; & Heath, R. W. (April 2023, 2023 IEEE Conference on Decision and Control)

   We propose an adaptive coding approach to achieve linear-quadratic-Gaussian (LQG) control with near- minimum bitrate prefix-free feedback. Our approach combines a recent analysis of a quantizer design for minimum rate LQG control with work on universal lossless source coding for sources on countable alphabets. In the aforementioned quantizer design, it was established that the quantizer outputs are an asymp- totically stationary, ergodic process. To enable LQG control with provably near-minimum bitrate, the quantizer outputs must be encoded into binary codewords efficiently. This is possible given knowledge of the probability distributions of the quantizer outputs, or of their limiting distribution. Obtaining such knowledge is challenging; the distributions do not readily admit closed form descriptions. This motivates the application of universal source coding. Our main theoretical contribution in this work is a proof that (after an invertible transformation), the quantizer outputs are random variables that fall within an exponential or power-law envelope class (depending on the plant dimension). Using ideas from universal coding on envelope classes, we develop a practical, zero-delay version of these algorithms that operates with fixed precision arithmetic. We evaluate the performance of this algorithm numerically, and demonstrate competitive results with respect to fundamental tradeoffs between bitrate and LQG control performance. 

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2. A Lower-Bound for Variable-Length Source Coding in Linear-Quadratic-Gaussian Control With Shared Randomness

   Cuvelier, T.C.; Tanaka, T.; & Heath, R.W. (June 2022, IEEE control systems letters)

   In this letter, we consider a Linear Quadratic Gaussian (LQG) control system where feedback occurs over a noiseless binary channel and derive lower bounds on the minimum communication cost (quantified via the channel bitrate) required to attain a given control performance. We assume that at every time step an encoder can convey a packet containing a variable number of bits over the channel to a decoder at the controller. Our system model provides for the possibility that the encoder and decoder have shared randomness, as is the case in systems using dithered quantizers. We define two extremal prefix-free requirements that may be imposed on the message packets; such constraints are useful in that they allow the decoder, and potentially other agents to uniquely identify the end of a transmission in an online fashion. We then derive a lower bound on the rate of prefix-free coding in terms of directed information; in particular we show that a previously known bound still holds in the case with shared randomness. We generalize the bound for when prefix constraints are relaxed, and conclude with a rate-distortion formulation. 

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3. Rate of Prefix-free Codes in LQG Control Systems with Side Information

   Cuvelier, T.C. & (March 2021, Annual Conference on Information Sciences and Systems (CISS))

   In this work, we study an LQG control system where one of two feedback channels is discrete and incurs a communication cost. We assume that a decoder (co-located with the controller) can make noiseless measurements of a subset of the state vector (referred to as side information) meanwhile a remote encoder (co-located with a sensor) can make arbitrary measurements of the entire state vector, but must convey its measurements to the decoder over a noiseless binary channel. Use of the channel incurs a communication cost, quantified as the time-averaged expected length of prefix-free binary codeword. We study the tradeoff between the communication cost and control performance. The formulation motivates a constrained directed information minimization problem, which can be solved via convex optimization. Using the optimization, we propose a quantizer design and a subsequent achievability result. 

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4. Sequential Source Coding for Stochastic Systems Subject to Finite Rate Constraints

   Stavrou, P.; Skoglund, M.; & Tanaka, T. (September 2021, IEEE transactions on automatic control)

   In this article, we revisit the sequential source-coding framework to analyze fundamental performance limitations of discrete-time stochastic control systems subject to feedback data-rate constraints in finite-time horizon. The basis of our results is a new characterization of the lower bound on the minimum total-rate achieved by sequential codes subject to a total (across time) distortion constraint and a computational algorithm that allocates optimally the rate-distortion, for a given distortion level, at each instant of time and any fixed finite-time horizon. The idea behind this characterization facilitates the derivation of analytical , nonasymptotic , and finite-dimensional lower and upper bounds in two control-related scenarios: a) A parallel time-varying Gauss–Markov process with identically distributed spatial components that are quantized and transmitted through a noiseless channel to a minimum mean-squared error decoder; and b) a time-varying quantized linear quadratic Gaussian (LQG) closed-loop control system, with identically distributed spatial components and with a random data-rate allocation. Our nonasymptotic lower bound on the quantized LQG control problem reveals the absolute minimum data-rates for (mean square) stability of our time-varying plant for any fixed finite-time horizon. We supplement our framework with illustrative simulation experiments. 

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5. Robust Wirtinger Flow Algorithm for Channel Coded Blind Demixing

   https://doi.org/10.1109/ICC45855.2022.9838429  

   Jalali, Amin; Shi, Yuanming; Ding, Zhi (March 2022, IEEE International Conference on Communications)

   As applications of Internet-of-things (IoT) rapidly expand, unscheduled multiple user access with low latency and low cost communication is attracting growing more interests. To recover the multiple uplink signals without strict access control under dynamic co-channel interference environment, the problem of blind demixing emerges as an important obstacle for us to overcome. Without channel state information, successful blind demixing can recover multiple user signals more effectively by leveraging prior information on signal characteristics such as constellations and distribution. This work studies how forward error correction (FEC) codes in Galois Field can generate more effective blind demixing algorithms. We propose a constrained Wirtinger flow algorithm by defining a valid signal set based on FEC codewords. Specifically, targeting the popular polar codes for FEC of short IoT packets, we introduce signal projections within iterations of Wirtinger Flow based on FEC code information. Simulation results demonstrate stronger robustness of the proposed algorithm against noise and practical obstacles and also faster convergence rate compared to regular Wirtinger flow algorithm. 

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