In this paper, a Look-Up-Table (LUT) based calculation for implementing log-likelihood ratio (LLR) of the Maximum a Posterior (MAP) decoder is introduced and analysed. In the region of low signal to noise ratio, the analysed performances of turbo coding have been found very satisfying. However, when implementing the MAP turbo decoder, the required calculation for LLR is too complex prohibiting its applications. In order to reduce the complexity a dynamic-LUT based simplification is proposed whereas a static-LUT never converge the expectations, since the limited size and resolution of LUT dramatically degrade the performance. In order to maintain simplicity for a high performance implementation, a dynamic LUT, which has partial resolutions in separate decision regions and being re-calculated for further iterations of decoding, is proposed. One of the most important results obtained is that our proposed dynamic-LUT based MAP algorithm removes "ln(center dot)" process, which is the natural logarithm in LLR's calculation. Therefore, it reduces high computational complexity in the MAP algorithm with some reasonable performance degradations.