Dyadic Probabilistic Shaping of PAM-4 and PAM-8 for Cost-Effective VCSEL-MMF Optical Interconnection

In this paper, dyadic probabilistic shaping (PS) for pulse amplitude modulation (PAM) has been investigated and experimentally demonstrated for intensity-modulation and direct-detection optical interconnection systems. Improved achievable information rate can be obtained under the condition of limited bandwidth and signal-to-noise ratio (SNR). Theoretical investigations of generalized mutual information have been performed. 0.61- and 1.74-dB SNR gains by dyadic PS can be obtained for PAM-4 and PAM-8, respectively, to achieve error free assuming optimal 20% FEC. Meanwhile, such fixed distributions can offer a considerably broad SNR range (10.3-16.7 dB for PAM-4 and 13.4-24.6 dB for PAM-8) with positive gain. Moreover, experimental investigations have been carried out over optical multimode fiber (MMF) links at 850 nm using a commercial-product-level vertical-cavity surface-emitting laser (VCSEL) chip. PAM-8 signaling by PS at the net rate of 75 Gb/s has been realized with 100-m OM3 fiber transmission. Energy efficient signaling can be achieved with up to 46% theoretical power reduction by PS. Experimentally, we obtained 16% reduction of optical power for the VCSEL-MMF optical link. The dyadic distribution of PS, due to its simplicity of coding, as well as considerable shaping gain and energy efficiency, is expected to be an opportune solution for the cost-sensitive short-reach scenarios.