Rate-distortion function via minimum mean square error estimation

We derive a simple general parametric representation of the rate-distortion function of a memoryless source, where both the rate and the distortion are given by integrals whose integrands include the minimum mean square error (MMSE) of the distortion $\Delta=d(X,Y)$ based on the source symbol $X$, with respect to a certain joint distribution of these two random variables. At first glance, these relations may seem somewhat similar to the I-MMSE relations due to Guo, Shamai and Verd\'u, but they are, in fact, quite different. The new relations among rate, distortion, and MMSE are discussed from several aspects, and more importantly, it is demonstrated that they can sometimes be rather useful for obtaining non-trivial upper and lower bounds on the rate-distortion function, as well as for determining the exact asymptotic behavior for very low and for very large distortion. Analogous MMSE relations hold for channel capacity as well.Comment: 11 pages, 1 figure, submitted for publication

A Survey on MIMO Transmission with Discrete Input Signals: Technical Challenges, Advances, and Future Trends

Multiple antennas have been exploited for spatial multiplexing and diversity transmission in a wide range of communication applications. However, most of the advances in the design of high speed wireless multiple-input multiple output (MIMO) systems are based on information-theoretic principles that demonstrate how to efficiently transmit signals conforming to Gaussian distribution. Although the Gaussian signal is capacity-achieving, signals conforming to discrete constellations are transmitted in practical communication systems. As a result, this paper is motivated to provide a comprehensive overview on MIMO transmission design with discrete input signals. We first summarize the existing fundamental results for MIMO systems with discrete input signals. Then, focusing on the basic point-to-point MIMO systems, we examine transmission schemes based on three most important criteria for communication systems: the mutual information driven designs, the mean square error driven designs, and the diversity driven designs. Particularly, a unified framework which designs low complexity transmission schemes applicable to massive MIMO systems in upcoming 5G wireless networks is provided in the first time. Moreover, adaptive transmission designs which switch among these criteria based on the channel conditions to formulate the best transmission strategy are discussed. Then, we provide a survey of the transmission designs with discrete input signals for multiuser MIMO scenarios, including MIMO uplink transmission, MIMO downlink transmission, MIMO interference channel, and MIMO wiretap channel. Additionally, we discuss the transmission designs with discrete input signals for other systems using MIMO technology. Finally, technical challenges which remain unresolved at the time of writing are summarized and the future trends of transmission designs with discrete input signals are addressed.Comment: 110 pages, 512 references, submit to Proceedings of the IEE

1 Rate–Distortion Function via Minimum Mean Square Error Estimation

Abstract—We derive a simple general parametric representation of the rate–distortion function of a memoryless source, where both the rate and the distortion are given by integrals whose integrands include the minimum mean square error (MMSE) of the distortion ∆ = d(X, Y) based on the source symbol X, with respect to a certain joint distribution of these two random variables. At first glance, these relations may seem somewhat similar to the I–MMSE relations due to Guo, Shamai and Verdú, but they are, in fact, quite different. The new relations among rate, distortion, and MMSE are discussed from several aspects, and more importantly, it is demonstrated that they can sometimes be rather useful for obtaining non–trivial upper and lower bounds on the rate–distortion function, as well as for determining the exact asymptotic behavior for very low and for very large distortion. Analogous MMSE relations hold for channel capacity as well. Index Terms—Rate–distortion function, Legendre transform, estimation, minimum mean square error