High Throughput Probabilistic Shaping with Product Distribution Matching

Product distribution matching (PDM) is proposed to generate target distributions over large alphabets by combining the output of several parallel distribution matchers (DMs) with smaller output alphabets. The parallel architecture of PDM enables low-complexity and high-throughput implementation. PDM is used as a shaping device for probabilistic amplitude shaping (PAS). For 64-ASK and a spectral efficiency of 4.5 bits per channel use (bpcu), PDM is as power efficient as a single fullfledged DM. It is shown how PDM enables PAS for parallel channels present in multi-carrier systems like digital subscriber line (DSL) and orthogonal frequency-division multiplexing (OFDM). The key feature is that PDM shares the DMs for lower bitlevels among different sub-carriers, which improves the power efficiency significantly. A representative parallel channel example shows that PAS with PDM is 0.93 dB more power efficient than conventional uniform signaling and PDM is 0.35 dB more power efficient than individual per channel DMs.