This paper investigates three types of adaptive bidirectional decision feedback equalizers (BiDFE) for the plastic optical fiber (POF) based high speed in-vehicle transmission for infotainment applications. We show that 2-3Gbit/s transmission speed can be reached with a 10m fiber length, using an light emitting diode (LED). BiDFE utilizes a forward DFE and a reverse DFE to equalize the received sequence and the time-reversed replica, and provides two decided symbol sequences. It uses then an arbitrator to choose from the two, the one which better explains the received sequence. Benefiting from the use of a reverse DFE, BiDFE can be superior to conventional DFE. Its performance is suboptimal compared to a posterior equalizer, but it is less complicated. Among the various BiDFE proposals, the bi-directional arbitrated DFE (BAD) and the trellis-based conflict resolution (TBCR) algorithm are specially considered in this paper. The simulation results show that they surpass conventional DFE by 1.5dB at bit error rate (BER) of 10^-3 for a 3Gbit/s transmission. However, both algorithms have shortages and their performances can be improved by a novel equalization scheme proposed in this paper, named as the trellis-based BiDFE (TB-BiDFE). TB-BiDFE outperforms conventional DFE by 2dB at BER of 10^-3 and TBCR by 1dB at BER of 10^-6 for a 3Gbit/s transmission. It has also a moderate complexity.