Bit error rate (BER) performance of convolutional coding/soft decision Viterbi decoding is investigated theoretically. Firstly, equations are derived to calculate the tight upper bound of the BER performance for the multi-level soft decision with arbitrary threshold spacing, considering the quantized metric used in the Viterbi decoder. Experimental results on the BER performance of a rate 1/2 code with constraint length 7 are shown to demonstrate that the derived equations provide the precise BER performance. Then, the BER performance of various codes is calculated for 4- and 8-level soft decision as well as hard decision and ideal (infinite level) soft decision. The codes examined in this paper cover typical codes with 64 states of rate 1/4 through 3/4 and the rate 1/2 codes with constraint length 3 through 14. From the BER curves obtained for these codes, the coding gain is clarified as a function of coding rate and code constraint length. Main results obtained in this paper are as follows. (1) Among codes with 64 states, rate 1/3 code gives the maximum coding gain. (2) Coding gain of a rate 1/2 code increases as constraint length K becomes large. In the case of 8-level soft decision, for instance, the coding gain of the code with K14 reaches 7.1 dB at BER10-6, which is close to the maximum coding gain obtained by an infinite constraint length code (estimated to be 7.9 dB).