Raptor Codes in the Low SNR Regime

In this paper, we revisit the design of Raptor codes for binary input additive white Gaussian noise (BIAWGN) channels, where we are interested in very low signal to noise ratios (SNRs). A linear programming degree distribution optimization problem is defined for Raptor codes in the low SNR regime through several approximations. We also provide an exact expression for the polynomial representation of the degree distribution with infinite maximum degree in the low SNR regime, which enables us to calculate the exact value of the fractions of output nodes of small degrees. A more practical degree distribution design is also proposed for Raptor codes in the low SNR regime, where we include the rate efficiency and the decoding complexity in the optimization problem, and an upper bound on the maximum rate efficiency is derived for given design parameters. Simulation results show that the Raptor code with the designed degree distributions can approach rate efficiencies larger than 0.95 in the low SNR regime.Comment: Submitted to the IEEE Transactions on Communications. arXiv admin note: text overlap with arXiv:1510.0772

Massive Non-Orthogonal Multiple Access for Cellular IoT: Potentials and Limitations

The Internet of Things (IoT) promises ubiquitous connectivity of everything everywhere, which represents the biggest technology trend in the years to come. It is expected that by 2020 over 25 billion devices will be connected to cellular networks; far beyond the number of devices in current wireless networks. Machine-to-Machine (M2M) communications aims at providing the communication infrastructure for enabling IoT by facilitating the billions of multi-role devices to communicate with each other and with the underlying data transport infrastructure without, or with little, human intervention. Providing this infrastructure will require a dramatic shift from the current protocols mostly designed for human-to-human (H2H) applications. This article reviews recent 3GPP solutions for enabling massive cellular IoT and investigates the random access strategies for M2M communications, which shows that cellular networks must evolve to handle the new ways in which devices will connect and communicate with the system. A massive non-orthogonal multiple access (NOMA) technique is then presented as a promising solution to support a massive number of IoT devices in cellular networks, where we also identify its practical challenges and future research directions.Comment: To appear in IEEE Communications Magazin

Design of First-Order Optimization Algorithms via Sum-of-Squares Programming

In this paper, we propose a framework based on sum-of-squares programming to design iterative first-order optimization algorithms for smooth and strongly convex problems. Our starting point is to develop a polynomial matrix inequality as a sufficient condition for exponential convergence of the algorithm. The entries of this matrix are polynomial functions of the unknown parameters (exponential decay rate, stepsize, momentum coefficient, etc.). We then formulate a polynomial optimization, in which the objective is to optimize the exponential decay rate over the parameters of the algorithm. Finally, we use sum-of-squares programming as a tractable relaxation of the proposed polynomial optimization problem. We illustrate the utility of the proposed framework by designing a first-order algorithm that shares the same structure as Nesterov's accelerated gradient method