Probabilistic Parity Shaping for Linear Codes

Linear layered probabilistic shaping (LLPS) is proposed, an architecture for linear codes to efficiently encode to shaped code words. In the previously proposed probabilistic amplitude shaping (PAS) architecture, a distribution matcher (DM) maps information bits to shaped bits, which are then systematically encoded by appending uniformly distributed parity bits. LLPS extends PAS by probabilistic parity shaping (PPS), which uses a syndrome DM to calculate shaped parity bits. LLPS enables the transmission with any desired distribution using linear codes, furthermore, by LLPS, a given linear code with rate $R_{\text{fec}}$ can be operated at any rate $R\le R_{\text{fec}}$ by changing the distribution. LLPS is used with an LDPC code for dirty paper coding against an interfering BPSK signal, improving the energy efficiency by 0.8 dB.