Disclosed are a turbo decoder, which applies a base-2 binary LogMAP algorithm in implementing a turbo decoder to thereby reduce the hardware requirement and implement a high-speed turbo decoder, which comprising a split for splitting the sum of two input state metrics into an integral and a decimal part; a comparator for comparing the integral parts of the two state metrics to extract a maximum and a minimum integer; a subtractor for obtaining a difference between the original integral part and the maximum or minimum integer value; a lookup table for calculating the sum of exponential terms of base-2 function in the decimal parts; a shifter for shifting only a decimal part with a smaller integral part by the difference; an adder for adding the decimal part and a decimal part with a larger integral part; a log pre-processing block for applying a base-2 logarithm on the decimal part to thereby obtain a final value for the decimal part; and an adder for adding the maximum integral value and the final value for the decimal part to thereby obtain a final value of the base-2 function.