On the Evaluation of the Polyanskiy-Poor-Verdu Converse Bound for Finite Blocklength Coding in AWGN

A tight converse bound to channel coding rate in the finite block-length regime and under AWGN conditions was recently proposed by Polyanskiy, Poor, and Verdu (PPV). The bound is a generalization of a number of other classical results, and it was also claimed to be equivalent to Shannon's 1959 cone packing bound. Unfortunately, its numerical evaluation is troublesome even for not too large values of the block-length n. In this paper we tackle the numerical evaluation by compactly expressing the PPV converse bound in terms of non-central chi-squared distributions, and by evaluating those through a an integral expression and a corresponding series expansion which exploit a method proposed by Temme. As a result, a robust evaluation method and new insights on the bound's asymptotics, as well as new approximate expressions, are given.Comment: 13 pages, 10 figures. Matlab code available from http://dgt.dei.unipd.it section Download->Finite Blocklength Regim

Coding in the Finite-Blocklength Regime: Bounds based on Laplace Integrals and their Asymptotic Approximations

In this paper we provide new compact integral expressions and associated simple asymptotic approximations for converse and achievability bounds in the finite blocklength regime. The chosen converse and random coding union bounds were taken from the recent work of Polyanskyi-Poor-Verdu, and are investigated under parallel AWGN channels, the AWGN channels, the BI-AWGN channel, and the BSC. The technique we use, which is a generalization of some recent results available from the literature, is to map the probabilities of interest into a Laplace integral, and then solve (or approximate) the integral by use of a steepest descent technique. The proposed results are particularly useful for short packet lengths, where the normal approximation may provide unreliable results.Comment: 29 pages, 10 figures. Submitted to IEEE Trans. on Information Theory. Matlab code available from http://dgt.dei.unipd.it section Download->Finite Blocklength Regim

Exact Spectral Analysis of Single-h and Multi-h CPM Signals through PAM decomposition and Matrix Series Evaluation

In this paper we address the problem of closed-form spectral evaluation of CPM. We show that the multi-h CPM signal can be conveniently generated by a PTI SM. The output is governed by a Markov chain with the unusual peculiarity of being cyclostationary and reducible; this holds also in the single-h context. Judicious reinterpretation of the result leads to a formalization through a stationary and irreducible Markov chain, whose spectral evaluation is known in closed-form from the literature. Two are the major outcomes of this paper. First, unlike the literature, we obtain a PSD in true closed-form. Second, we give novel insights into the CPM format.Comment: 31 pages, 10 figure

A distributed approach to the OPF problem

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The final version of this manuscript will appear in IEEE Wireless Communication Letters

Abstract-This letter investigates the structure of the optimal policy for a class of Markov decision processes (MDPs), having convex and piecewise linear cost function. The optimal policy is proved to have a piecewise linear structure that alternates flat and constant-slope pieces, resembling a staircase with tilted rises and as many steps (thresholds) as the breakpoints of the cost function. This particular structure makes it possible to express the policy in a very compact manner, particularly suitable to be stored in low-end devices. More importantly, the thresholdbased form of the optimal policy can be exploited to reduce the computational complexity of the iterative dynamic programming (DP) algorithm used to solve the problem. These results apply to a rather wide set of optimization problems, typically involving the management of a resource buffer such as the energy stored in a battery, or the packets queued in a wireless node

The real-time optimisation of DNO owned storage devices on the LV network for peak reduction

Energy storage is a potential alternative to conventional network reinforcementof the low voltage (LV) distribution network to ensure the grid’s infrastructure remainswithin its operating constraints. This paper presents a study on the control of such storagedevices, owned by distribution network operators. A deterministic model predictive control (MPC) controller and a stochastic receding horizon controller (SRHC) are presented, wherethe objective is to achieve the greatest peak reduction in demand, for a given storagedevice specification, taking into account the high level of uncertainty in the prediction of LV demand. The algorithms presented in this paper are compared to a standard set-pointcontroller and bench marked against a control algorithm with a perfect forecast. A specificcase study, using storage on the LV network, is presented, and the results of each algorithmare compared. A comprehensive analysis is then carried out simulating a large number of LV networks of varying numbers of households. The results show that the performance of each algorithm is dependent on the number of aggregated households. However, on a typical aggregation, the novel SRHC algorithm presented in this paper is shown to outperform each of the comparable storage control techniques

Using Network Dynamical Influence to Drive Consensus

Consensus and decision-making are often analysed in the context of networks, with many studies focusing attention on ranking the nodes of a network depending on their relative importance to information routing. Dynamical influence ranks the nodes with respect to their ability to influence the evolution of the associated network dynamical system. In this study it is shown that dynamical influence not only ranks the nodes, but also provides a naturally optimised distribution of effort to steer a network from one state to another. An example is provided where the "steering" refers to the physical change in velocity of self-propelled agents interacting through a network. Distinct from other works on this subject, this study looks at directed and hence more general graphs. The findings are presented with a theoretical angle, without targeting particular applications or networked systems; however, the framework and results offer parallels with biological flocks and swarms and opportunities for design of technological networks

Coding Bounds in the Finite-Black-Length Regime: An Application to Spread-Spectrum Systems Design

Recent advances in coding theory have identified compact and tight bounds to the best achievable performance of an encoder/decoder couple in the practical case where codewords have a finite length. Such bounds are able to capture the essence of the physical layer without the need of designing and testing its constituent blocks (e.g., the encoder and decoder), and are thus perfectly suited for system design. In this paper we show how these bounds can be used to infer optimal parameters of a communication system based on a spread-spectrum technique, where the fundamental question is to identify a reasonable balance between the encoding process (i.e., the codeword length) and the length of the spreading sequence. The idea is exemplified in the context of the GNSS data component. However, it has a much wider range of applicability, especially in today's effort towards heterogeneous communications using short-packets where the results in the finite-length-regime play the role once played, in more traditional communication systems, by Shannon's capacity

Digital modulation systems

The term modulation denotes the process of transforming the information generated by a source into a signal that is suitable for transmission over a physical channel, in order to convey it to a receiver. When the information is represented by a sequence of bits, {b_\u2113}, we talk of digital modulation. The binary sequence detected by the receiver, {c_\u2113}, may well be affected by errors, i.e. c_\u2113 ~= b_\u2113 for some values of \u2113, due to distortion and noise introduced by the transmission medium. In this chapter we present a survey of the main modulation techniques used in modern digital communication systems (e.g., PAM, PSK, QAM, etc.). The performance of each modulation/demodulation method is evaluated with reference to the bit error probability, Pbit = P[c_\u2113 ~= b_\u2113], and a comparison of the various approaches is given

A distributed algorithm for fast optimal power flow regulation in Smart Grids

This paper deals with the solution of the optimal power flow (OPF) problem under voltage regulation by means of a distributed algorithm. Taking inspiration from the recent literature on distributed-OPF, the approach is developed via the alternating direction method of multipliers (ADMM), and provides a fully decentralized, scalable, very fast, and robust method, whose performance is shown in meaningful scenarios. Unlike most of the literature, no semi-definite programming (SDP) relaxations of the OPF problem is used, but local sub- problems are addressed via efficient interior point methods (IPMs) to guarantee limited local processing efforts