Place black barley and 4 cups of water in a small pot and bring t a boil. Reduce heat, cover and simmer until barley is soft and plump, approximately 50 minutes. Drain well and set aside. While barley is cooking, add vegetable stock, onion, celery, mushrooms and carrots to a 3 quart pot and cook over medium heat for 20 minutes, stirring occasionally. Add red pepper and corn, cook for 10 more minutes, stirring occasionally. Place miso soup in a small bowl with 1 cup of broth from the pot and stir well. Return to pot. Add remaining ingredients including black barley and stir well.