How can I assign my scroll wheel to a specific keystroke?

I have a logitech g500 which has some great customization options. I can bind just about anything on the mouse to do anything I want. However, something that is missing from the options is a way to assign scroll wheel up and scroll wheel down to something specific. I can assign tilting the wheel left or right to something, but I'm looking for a way to do it with the actual rolling of the wheel. Can I download some generic third party software that can take care of this for me?