Simple Deshaping Scheme to suppress Burst Error for Probabilistic Amplitude Shaping

Probabilistic amplitude shaping (PAS) is a practical architecture realizing probabilistic shaping to overcome the signal-noise ratio (SNR) gap toward Shannon limit. In PAS, the deshaper causes the burst errors which are multiple and consecutive errors in the output when the deshaper input has a residual error. To deal with the error enhancement due to burst error, we propose the error-correctable amplitude shaper based on enumerative sphere shaping (ESS), called error-correctable ESS (E-ESS). E-ESS requires soft-output forward error correction code to use the soft-information in the deshaping process. It can detect and correct a residual error in the deshaper input by restricting the number of "1"s in binary bits corresponding amplitude block and using the amplitude readjusting scheme. EESS has the rate loss penalty to ESS because of the restriction of amplitude block. This leads to the SNR penalty of E-ESS from ESS. Numerical simulation shows that E-ESS suppresses the error enhancement. In addition, it outperforms ESS at the appropriate length of amplitude block.