  Distribution matching (DM) transforms independent and Bernoulli(1/2)
distributed bits into a sequence of output symbols with a desired distribution.
A fixed-to-fixed length, invertible DM architecture based on shell mapping is
presented. It is shown that shell mapping for distribution matching (SMDM) is
the optimum DM for the informational divergence metric and that finding energy
optimal sequences is a special case of divergence minimization. Additionally,
it is shown how to find the required shell mapping weight function to
approximate arbitrary output distributions. SMDM is combined with probabilistic
amplitude shaping (PAS) to operate close to the Shannon limit. SMDM exhibits
excellent performance for short blocklengths as required by ultra-reliable
low-latency (URLLC) applications. SMDM outperforms constant composition DM
(CCDM) by 0.6 dB when used with 64-QAM at a spectral efficiency of 3
bits/channel use and a 5G low-density parity-check code with a short
blocklength of 192 bits
