Add data-icon input to Wordpress custom menu links

I need to add a data-icon="" input to my Wordpress Custom Menu input box thing. This is so I can use an icon font and type the code in for a specific icon and in the CSS use pseudo elements to match it up and display the icon.

I've found loads of tutorials which show how to extend the Walker_Nav_Menu class so I can add an attribute, but none of them extend this into adding a new input box on the Wordpress Custom Menu screen (http://cl.ly/Sn0C) and then having the value of this displayed in the HTML.

I've used this code to add a data-icon input box on the Custom Menu admin screen (http://cl.ly/SmqM) but I'm not good enough at PHP to link it up to the Walker_Nav_Menu extension class to show the data-icon value in the HTML. Can anyone help me out? Thanks :)

I would prefer if this could be done in functions.php and/or without the use of a plugin. Thanks!

Btw, here is my Walker_Nav_Menu extension class code:

class data_type_walker extends Walker_Nav_Menu {
      function start_el($output, $item, $depth, $args) {
           global $wp_query;
           $indent = ( $depth ) ? str_repeat( "\t", $depth ) : '';

           $class_names = $value = '';

           $classes = empty( $item-classes ) ? array() : (array) $item-classes;

           $class_names = join( ' ', apply_filters( 'nav_menu_css_class', array_filter( $classes ), $item ) );
           $class_names = ' class="'. esc_attr( $class_names ) . '"';

           $output .= $indent . 'li id="menu-item-'. $item-ID . '"' . $value . $class_names .'';

           $attributes  = ! empty( $item-attr_title ) ? ' title="'     . esc_attr( $item-attr_title       ) .'"' : '';
           $attributes .= ! empty( $item-target )     ? ' target="'    . esc_attr( $item-target           ) .'"' : '';
           $attributes .= ! empty( $item-xfn )        ? ' rel="'       . esc_attr( $item-xfn              ) .'"' : '';
           $attributes .= ! empty( $item-url )        ? ' href="'      . esc_attr( $item-url              ) .'"' : '';
           $attributes .= ! empty( $item-data_icon )  ? ' data-icon="' . esc_attr( $item-data_icon        ) .'"' : '';

           $prepend = '';
           $append = '';

           if($depth != 0) {
                 $description = $append = $prepend = "";
           }

            $item_output = $args-before;
            $item_output .= 'a'. $attributes .' aria-hidden="true"';
            $item_output .= $args-link_before .$prepend.apply_filters( 'the_title', $item-title, $item-ID ).$append;
            $item_output .= $description.$args-link_after;
            $item_output .= '/a';
            $item_output .= $args-after;

            $output .= apply_filters( 'walker_nav_menu_start_el', $item_output, $item, $depth, $args );
        }
}

EDIT: Chittaranjan asked me for some more info so here goes:

I'm calling this new extension (data_type_walker) on the class Walker_Nav_Menu in my header.php file where my nav menu is located. Calling it as follows:

?php wp_nav_menu( array( 'theme_location' = 'primary', 'container' = false, 'menu_class'= 'nav-menu', 'walker' = new data_type_walker() ) ); ?

The output should be something like this:

li class="all the various wordpress menu classes"a href="url" data-icon="whatever input I choose in the Custom Menu Admin section" aria-hidden="true"navigation text link/a/li