We propose and numerically demonstrate a photonic time-delay reservoir computing (TDRC) system exhibiting enhanced parallel task processing performance, where an optically injected vertical-cavity surface-emitting laser (VCSEL) under random distributed optical feedback acts as the reservoir computer. To assess its effectiveness, we perform two benchmark tasks including chaotic time-series prediction and waveform recognition task, where the TDRC is associated with two different random feedback structures, i.e., orthogonally polarized optical feedback (OPOF) and parallelly polarized optical feedback (PPOF). Benefiting from the enhanced nonlinearity offered by the random distributed optical feedback, the proposed TDRC excels at parallel task processing with the PPOF structure, whereas the performance of the OPOF structure may be deteriorated. Additionally, we reveal the effect of the injection strength, feedback strength, pump current, and number of virtual nodes on the proposed TDRC. Our work paves the way for the performance enhancement of parallel task processing based on polarization multiplexing in a VCSEL-based TDRC.
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