The LHCb experiment studies B-decays at the LHC. The Outer Tracker straw tubes detects charged decay particles. The on-detector electronics will be upgraded to be able to digitize and transmit drift-times at every LHC crossing without the need for a hardware trigger. FPGAs have been preferred to application-specific integrated circuits to implement dead-time free TDCs, able to transmit data volumes of up to 36 Gbits/s per readout unit, including the possibility of performing zero suppression. Extensive irradiation tests have been carried out to validate the usage of field-programmable devices in the hostile environment of the LHCb tracking system.