Inter-symbol interference (ISI) in wireless communication can cause signal distortion and increased bit error rate, thereby degrading system reliability and transmission efficiency. This paper addresses single-input single-output (SISO) channels with ISI by extending the classical one-dimensional real-domain Schalkwijk-Kailath (SK) coding scheme to the two-dimensional complex domain, proposing a novel linear feedback coding scheme to mitigate ISI. An auxiliary-variable-based update strategy is introduced, which combines minimum mean square error (MMSE) estimation and feedback mechanisms to iteratively refine the message estimate and eliminating interference from historical residuals. We derive the channel capacity and achievable rate, analyze the corresponding decoding error probability, and find that the proposed scheme achieves low error probabilities with relatively short blocklength. Numerical results demonstrate that the achievable rate can approach the channel capacity when the blocklength is sufficiently large. Moreover, the signal-to-noise ratio (SNR) can enhance channel throughput. This complex-domain SK-type coding scheme effectively reduces decoding error probability and enhances channel quality, offering an efficient coding scheme for communication system.