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This paper discusses the parallel propagation algorithm applied to the decoding of convolutional codes. The parallel algorithm surpasses the BCJR algorithm in parallel computational complexity and performance when it is applied to tail-biting codes. The complexity of iterative decoding algorithms depends on the calculation of posterior probability and bit error probability by using clique and number of iterations. The computational complexity of the parallel algorithm for tail-biting codes is almost the same as that for zero-tail convolutional codes.