Do you notice a particular time of day when he goes? Dixie and Dusty are both on a morning Poo schedule. Sometimes one of them will go later in the day too but it's always in the morning. If you determine a particular time of day, you can make sure your dog is outside then.

Dogs do not have to poo just because they ate their dinner. It takes a while for the food to digest and then travel through the intestines (usually 6 hours or so) before what they ate will be ready to come back out.

I would crate train the dog until it understood potty is outside and not on the carpet. If done correctly most dogs over the age of 12 weeks can catch on really quick if it's done correctly. If your dog will not poo after exercising for about 15 minutes, then bring him in the house and either crate him or teather him to you with a loose leash. Until there is a poo outside there is no house freedom. Make a big fuss over him when what you desire is accomplished.