Comparison and Optimization of Enumerative Coding Techniques for Amplitude Shaping - Gultekin, Yunus Can; van Houtum, Wim J.; Koppelaar, Arie G. C.; Willems, Frans M. J. (IEEE communications letters, 2021)
The energy efficiency of enumerative coding algorithms is investigated for amplitude shaping in the context of binary transmission. First, a simple method for the calculation of the amplitude distribution is derived for enumerative sphere shaping (ESS). For ultra-short blocklengths, ESS-which orders sequences lexicographically-is shown to be less energy-efficient than algorithms that use energy-based ordering such as shell mapping. Second, ESS is optimized heuristically such that its energy efficiency is improved. Simulations show that optimized ESS achieves the same error probabilities as energy-based ordering methods for the additive white Gaussian noise (AWGN) channel, even at ultra-short blocklengths.