In a large mixing bowl stir together jicama, cucumber, sweet pepper, vinegar, and sugar. Cover and chill.
Rub salmon with oil; sprinkle with salt and red pepper. Heat a large cast-iron skillet or heavy, nonstick skillet. Cook fish, uncovered, over medium heat for 6 minutes per side or until fish just flakes with a fork. Serve immediately, or cover and chill before serving.
To serve, overlap 2 or 3 lettuce leaves each on 4 dinner plates. Top with 2 salmon pieces. Spoon about 2 tablespoons of the jicama and sweet pepper salsa over fish. Makes 4 main-dish servings.