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Constant Composition Distribution Matching

Distribution matching transforms independent and Bernoulli(1/2) distributed input bits into a sequence of output symbols with a desired distribution. Fixed-to-fixed length, invertible, and low complexity encoders and decoders based on constant composition and arithmetic coding are presented. Asymptotically in the blocklength, the encoder achieves the maximum rate, namely the entropy of the desired distribution. Furthermore, the normalized divergence of the encoder output and the desired distribution goes to zero in the blocklength.