You should send the resignation letter giving your date of release,say after 30 days, as mentioned in your appointment letter.You should then follow up by giving another letter, say after 20 days,giving reference of your previous letter.In the letter, you mention valid reasons why you seek an early release.By continuous pursuance with your boss and HR department,you can secure your release within the notice period.At the most there may be a delay of a few days,which you should accommodate.