The use of wireless implanted medical devices is growing because they reduce the discomfort of patients and the likelihood of infection associated with trailing wires. Currently, radiofrequency electromagnetic waves are the most commonly used method for communicating wirelessly with IMDs. However, due to the restrictions on the available bandwidth and transmitted power, the data rates of RF-based IMDs are limited. Previously, we introduced signal processing and communications methods that use phase-coherent decision feedback equalization to relay information robustly at high data rates using ultrasonic waves. The experiments performed with ex vivo biological tissues in a water tank demonstrated data rates greater than 4 Mbps with bit error rate less than 1e-4 using mm-sized, biocompatible transducers. In this study, we first employ the proposed system in simulations conducted with finite impulse response channel models obtained with mm-sized transducers in phantoms and demonstrate video-capable data rates at moderate signal-to-noise ratio levels. We then perform in situ and in vivo physical experiments with rabbits, and achieve 3.2 and 6.2 Mbps data rates, respectively. Finally, we quantify the degrading effects of acoustic nonlinearities on the data rates by using nonlinear propagation models for biological tissues, and we propose ways to mitigate such effects.