Low-Complexity Enumerative Coding Techniques With Applications to Amplitude Shaping

Practical implementation of enumerative sphere shaping (ESS) is considered. First, an on-the-fly computation method is proposed such that the required storage is significantly decreased, e.g., by a factor of 7 for 8-ary amplitude-shift keying (ASK) at blocklength N = 64 and shaping rate of 1.75 bit/amplitude. Then a sliding window shaping (SWS) architecture is introduced to eliminate the necessity to realize high precision arithmetic operations, and to decrease the computational complexity of ESS. The SWS procedure only requires three 16-bit arithmetic operations per output symbol for 8-ASK.