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This paper considers the Z-channel, which is known as a channel model for photon communication or semiconductor memory. A new decoding algorithm is proposed and discussed. Recently, studies have been made from various viewpoints on the asymmetrical error-correcting code suited to the Z-channel, which is considered interesting. One of the basic problems in the Z-channel is the performance and the decoding method when the cyclic code with various features is applied, but it has been investigated little. This paper presents first a maximum-likelihood decoding algorithm which is highly efficient for the cyclic code on the Z-channel. It is then shown that by providing a certain threshold for the algorithm, a higher-speed decoding is realized. It is shown also that by setting the threshold above a certain value, the computational complexity can be improved without sacrificing the maximum-likelihood property. Finally, it is demonstrated by numerical calculation that the decoding error probability is improved greatly by the decoding algorithm proposed in this paper, together with a drastic improvement in the computational complexity. [ABSTRACT FROM AUTHOR]