You will need some stabilizer, but in a 16,000 gallon pool, I'd start with 4 lbs. which should get you around 30ppm. You may decide later to bump it up to 40 or 50, but 30 is a good starting place.

Try and sustain your shock level for your chlorine by testing 2 or even 3(better!) times a day and each time shock it back up. If you let the cl level yo-yo up and down, you'll never clear the pool.

However, I wouldn't add it just yet. I would wait until you take care of the algae problem.