Dual Coding Concatenation for Burst-Error Correction in Probabilistic Amplitude Shaping

We propose the use of dual coding concatenation for mitigation of post-shaping burst errors in probabilistic amplitude shaping (PAS) architectures. The proposed dual coding concatenation for PAS is a hybrid integration of conventional reverse concatenation and forward concatenation, i.e., post-shaping forward error correction (FEC) layer and pre-shaping FEC layer, respectively. A low-complexity architecture based on parallel Bose–Chaudhuri–Hocquenghem (BCH) codes is introduced for the pre-shaping FEC layer. Proposed dual coding concatenation can relax bit error rate (BER) requirement after post-shaping soft-decision (SD) FEC codes by an order of magnitude, resulting in a gain of up to 0.25 dB depending on the complexity of post-shaping FEC. Also, combined shaping and coding performance was analyzed based on sphere shaping and the impact of shaping length on coding performance was demonstrated.