Plasmonic waveguides have been widely studied in the rapid development of optically integrated circuits. The cross talk between plasmonic waveguides is a critical issue that should be considered. Nano-plasmonic waveguides with tunable graphene-free patterns on silicon ridge have very attractive features. Despite these attractive features, the low confinement in plasmonic waveguides reduces the coupling length. This issue results in high cross talk in optical integrated circuits. We present a solution to the mentioned problem. A metal ridge under the plasmonic channel helps to reduce the cross-talk value. A new graphene-based plasmonic waveguide has been proposed for achieving the switching operation at terahertz frequencies. Based on the designed waveguide, a 4-to-2 plasmonic encoder with the cross talk of -17.33dB has been presented. Using six waveguides, the encoder is designed with a contrast ratio of 14.44 dB and an area of 0.36µm2. Concerning the obtained results, the presented structure can be used in optical integrated circuits.