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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 ispresented. It is shown that shell mapping for distribution matching (SMDM) isthe optimum DM for the informational divergence metric and that finding energyoptimal sequences is a special case of divergence minimization. Additionally,it is shown how to find the required shell mapping weight function toapproximate arbitrary output distributions. SMDM is combined with probabilisticamplitude shaping (PAS) to operate close to the Shannon limit. SMDM exhibitsexcellent performance for short blocklengths as required by ultra-reliablelow-latency (URLLC) applications. SMDM outperforms constant composition DM(CCDM) by 0.6 dB when used with 64-QAM at a spectral efficiency of 3bits/channel use and a 5G low-density parity-check code with a shortblocklength of 192 bits

Divergence-Optimal Fixed-to-Fixed Length Distribution Matching With Shell Mapping