Finite-precision implementation of arithmetic coding based distribution matchers

A distribution matcher (DM) encodes a binary input data sequence into a sequence of symbols with a desired target probability distribution. Several DMs, including shell mapping and constant- composition distribution matcher (CCDM), have been successfully employed for signal shaping, e.g., in optical-fiber or 5G. The CCDM, like many other DMs, is typically implemented by arithmetic coding (AC). In this work we implement AC based DMs using finite-precision arithmetic (FPA). An analysis of the implementation shows that FPA results in a rate-loss that shrinks exponentially with the number of precision bits. Moreover, a relationship between the CCDM rate and the number of precision bits is derived.