In LHC Run 3, the upgraded ALICE detector will record 50 kHz Pb-Pb collisions using continuous readout. The resulting stream of raw data to be inspected increases to ~ 1 TB/s a hundredfold increase over Run 2 must be processed with a set of lossy and lossless compression and data reduction techniques to decrease the data rate to storage to 90 GB/s without affecting the physics. This contribution focuses on lossless entropy coding for ALICE Run 3 data which is the final component in the compression stage. We analyze data from the ALICE TPC and point out the challenges imposed by the non-standard data with a patchy distribution and symbol sizes of up to 25 Bit. We then explain why rANS, a variant of Asymmetric Numeral System coders is suitable for compressing this data effectively. Finally we present first compression performance numbers and bandwidth measurements obtained from a prototype implementation and give an outlook for future developments.