This paper describes the application of an adaptive complexity decoder for the Long Term Evolution (LTE) downlink Turbo code. The proposed decoding approach is based on the block syndrome decoding principle and enables adaptive reduction of decoding effort depending on current SNR and iteration number with negligible influence on decoding performance. Numerical results in context of LTE downlink using typical mobile channels are used to demonstrate the efficiency of the approach. The iterative decoder of Turbo Trellis Coded Modulation (TTCM) exchanges extrinsic information between the constituent TCM decoders, which imposes a high computational complexity at the receiver. Therefore we conceive the syndrome-based block decoding of TTCM, which is capable of reducing the decoding complexity by disabling the decoder, when syndrome becomes zero. Quantitatively, we demonstrate that a decoding complexity reduction of at least 17% is attained at high SNRs, with at least 20% and 45% reduction in the 5th and 6th iterations, respectively. In order to reduce its decoding complexity, we propose to reduce the effective number of decoding iterations by appropriately adapting the syndrome based block decoding approach for TTCM