Trellis-Based Error-Correctable Shaping Method for Probabilistically-Shaped Quadrature Amplitude Modulation

This letter proposes the error-correctable shaping method based on the trellis diagram defined in enumerative sphere shaping (ESS), refer to trellis-based error-correctable ESS (TE-ESS), to mitigate one of the implementation issues in probabilistic amplitude shaping (PAS). To introduce the residual error detection and correction, TE-ESS modifies the trellis diagram of ESS to restrict the output amplitude sequence which correspond to even-or odd-parity. Numerical simulations show that TE-ESS outperforms the previously proposed error-correctable shaping method. In addition, Its error correction effectively alleviates the error floor requirement in FEC code, compared to using ESS, in low BER region.