The cloud radio access network (C-RAN) mitigates inter-cell interference by jointly processing the observations of distributed remote units (RUs) at a centralized unit (CU), but limited fronthaul capacity forces each RU to compress its received signal. Under transform-compress-forward, an RU transforms its signal and quantizes the resulting coefficients, with bit allocation distributing a finite bit budget across them. Classical reverse waterfilling assumes Gaussian sources, yet practical finite-alphabet symbols carry mutual information that saturates at $\log_2 M$, leaving bit allocation for such inputs unresolved. We address this by formulating bit allocation as maximizing the finite-alphabet generalized mutual information (GMI) achieved after linear MMSE (LMMSE) detection at the CU. Via the I-MMSE relation, this yields a fixed-point update whose converged solution decomposes into a vessel height, a shared water level, and a finite-alphabet mercury level; we term it {reverse mercury/waterfilling} (RMWF). Numerical results show that RMWF sustains end-to-end rate under tight fronthaul budgets and remains robust under antenna scaling, which is increasingly consequential as antenna counts outpace fronthaul capacity in modern C-RAN.

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