In a large bowl, whisk together flour, cornstarch, baking soda, egg and 1/2 cup of the ice water.
Whisk in remaining water, 1/4 cup at a time, to make thin batter. Stir in corn. Place bowl, in second bowl filled with more ice water.
Pour enough oil into wok or Dutch oven to come about 2-inches up side; heat until deep fryer thermometer reads 375F or until 1-inch cube of white bread turns golden in 30 seconds.
Gently drop batter 2 Tablespoons at a time, into hot oil (batter will sink slightly then rise to surface with bits breaking off at edges). Deep-fry, turning once, until golden brown, about 3 minutes. Drain on paper towel-lined rack.
DIPPING SAUCE: In small saucepan, bring dipping sauce and water to boil; remove from heat. Squeeze out liquid from radish; add radish to sauce. Serve with tempura.