Combine sugar and 1 cup of water in a small saucepan.

Cook over medium heat, stirring until sugar dissolves (3-4 minutes).

Remove from heat and cool to room temperature (about 30 minutes).

Place raspberries and lime juice in a food processor.

Process until smooth.

Strain raspberry mixture through a fine wire-mesh sieve over a bowl.

Press solids to extract liquid and discard the solids.

Stir cooled sugar mixture into the raspberry mixture.

Stir in ginger.

Transfer to a 13- x 9-inch glass baking dish.

Freeze, stirring every 15 minutes, until almost firm (about 1 hour).

Freeze without stirring until firm (2 hours or overnight).

Sorbet may be frozen, covered, for up to 1 week.