We give a general procedure for constructing shaping codes from costly constrained graphs. The codes have finite-state encoders and sliding-block decoders. The shaping codes are in the spirit of Calderbank and Ozarow (1990), where shaping is achieved by nonequiprobable signaling on T subconstellations of a signal constellation /spl Omega/. We show how nonequiprobable signaling relates to a costly constrained channel. Khayrallah and Neuhoff developed a procedure for constructing codes with rates close to the capacity-cost function of the general cost-constrained channel, and we use their procedure to construct asynchronous (variable-length to fixed-length) shaping codes. Comparisons are made with shaping codes having comparable gain. The codes presented here are less complex and have lower peak-to-average power and lower constellation expansion ratio.
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