So for I was thinking that the problem is with Star Group HD Channels. But the fact is different, Being Sunday I made few tests to pin point the problem today.
I am having Samsung 40 Inch LED (6900), AirTel HD STB and Samsung 1000W 3D Bluray Home theatre (5530), The connection follows like this : STB to TV thro HDMI Cable, TV to Home Theatre thro Optical Cable. Now when my setting in STB is audio thro HDMI is set as DD Plus, star group channels no out putting. Other HD channels out puts are fine. When I change the setting to DD star channels are also fine. So I thought problem is with Star HD Channels. Today I changed the connection as follows: STB to Home Theatre thro Optical Cable. Now every thing is fine. When I set STB as Audio thro HDMI is DD Plus all the channels including Star HDs are fine. I get DD Plus audio, but I could not find much difference between DD and DD Plus. So I confirm that the problem is my TV is not able to deliver DD Plus It delivers only DD 5.1. The another shocking truth is All other HD channels except Star Group channels are NOT DD Plus but only DD.