1. Combine sugar and 1 cup water in a small saucepan, and cook over medium heat, stirring often, 3 to 4 minutes or until sugar dissolves. Remove pan from heat, and let cool to room temperature, about 30 minutes.
2. Place raspberries and lime juice in a food processor, and process until smooth. Strain raspberry mixture through a fine wire-mesh sieve placed over a bowl, pressing solids with a wooden spoon to extract liquid. Discard solids.
3. Stir cooled sugar mixture into raspberry mixture; stir in ginger. Transfer to a 13- x 9-inch glass baking dish.
4. Freeze, stirring every 15 minutes, until almost firm, about 1 hour. Freeze (without stirring) until firm, 2 hours or overnight. May be frozen, covered, for up to 1 week.