Grate enough of the radish to yield 1/4 cup. Add this to the orange juice and soy sauce mixture. Mix well, along with the sugar, and chill.
Cut the chicken pieces into bite-sized pieces and simmer in chicken stock. Cover and simmer for one hour, or until the chicken is tender and falling off of the bones. Cut the radish into slices 1/2 inch thick. Slice the cabbage. Cut the mushrooms in half. Dice the tofu into 1 inch cubes. Add to the broth in the last 15 minutes of cooking.
Serve in individual bowls, with saucers of the chilled soy-orange sauce, scallions, and salt for dipping.