Deeply implanted bioelectronic devices that selectively record and stimulate peripheral nerves have the potential to revolutionize healthcare by delivering on-demand, personalized therapy. A key barrier to this goal is the lack of a miniaturized, robust, and energy-efficient wireless link capable of transmitting data from multiple sensing channels. To address this issue, we present a wireless galvanic impulse link that uses two 500μm diameter planar electrodes on the outside of a nerve cuff to transmit data to a wearable receiver on the skin's surface at rates greater than 1Mbps. To achieve an energy-efficient, high data rate link, our protocol encodes information in the timing of narrow biphasic pulses that is reconstructed by the wearable receiver. We use a combination of modeling and in vivo and in vitro experimentation to demonstrate the viability of the link. We demonstrate losses lower than 60dB even with significant, 50mm lateral misalignment, ensuring a sufficient signal-to-noise ratio for robust operation. Using a custom, flexible nerve cuff, we demonstrate data transmission in a 14mm-thick rodent animal model and in a 42mm-thick heterogeneous human tissue phantom.