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In this paper, we investigate the second-order statistics of the matched information rate code (MIRC) sequence. Recently, a serial concatenation coding scheme was proposed to approach the capacity of a partial response (PR) channel, which is a basic model for digital recording systems. In this paper, we compute the power spectral density (p.s.d.) of the suboptimal binary input process concentrate in the frequency band where the water-filling solution(Gaussian channel) does not vanish and has low-powers(but not zero) at channel spectral s.