Modern communication systems that employ LDPC codes and QAM modulation can achieve high speed and reliable transmission without bandwidth expansion. In this paper, the performances of LDPC codes with 2m- ary QAM at m>10, which can provide enormous bandwidth efficiency, are studied. Bit error rate performances of various combinations of LDPC codes and order of QAM are provided. From the results, the performance of LDPC coded ultra-high order QAM is excellent making this system very attractive for ultra-high speed communications.