In this paper, we derive a capacity inner bound for a synchronous Gaussian Z channel with intersymbol interference (ISI) under input power constraints. This is done by converting the original channel model into an n-block memoryless circular Gaussian Z channel (n-CGZC) and successively decomposing the n-block memoryless channel into a series of independent parallel channels in the frequency domain using the discrete Fourier transform (DFT). The capacity inner bounds for these parallel channels can be determined easily. Since we assume that our channel is a synchronous channel, the capacity inner bound of the Gaussian Z channel with ISI is the same as the capacity inner bound of the n-CGZC in the limit of infinite block length. Moreover, some numerical results showing the loss in rate caused by ISI are given.

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