Approximate Enumerative Sphere Shaping

Enumerative sphere shaping of N-dimensional constellations is discussed. It is proven that a finite-precision number representation is suitable for use in two enumerative indexing algorithms: Enumerative sphere shaping and Divide & Conquer (D&C) shaping. This representation decreases the storage complexities of these methods significantly. D&C is the basis of the well-known shell mapping algorithm and thus our approximations also apply there.