In a 4-quart saucepan over medium heat, cook the bacon until just crisp, stirring occasionally. With a slotted spoon, remove it and place on paper towels to drain. Reserve bacon.
Leave 2 tablespoons bacon drippings in the saucepan. Add the celery, potatoes, onion and pepper, and cook on medium heat, then switch to low when mixture begins to simmer. Cook until vegetables are just tender, about 5 minutes, stirring occasionally. Stir in flour and paprika; cook 1 minute.
Gradually stir in the chicken broth and salt until mixture is smooth and thickened.
Stir in the corn and either the half & half or heavy whipping cream. Over high heat, heat to boiling. Reduce heat to low; simmer uncovered 5–10 minutes, until the mixture is heated through.
To serve, sprinkle each serving with reserved bacon.