This paper considers a $K$ -user single-input-single-output (SISO) interference channel with inter-symbol interference (ISI), in which the channel coefficients are assumed to be linear time-invariant with finite-length impulse response. The key finding of this paper is that, with no channel state information at the transmitter (CSIT), the sum-spectral efficiency can be made to scale linearly with $K$ , provided that the desired links have longer impulse responses than do the interfering links. This linear gain can be achieved (up to the maximum gain of $\frac{K}{2}$ for a particular case) by a novel multi-carrier communication scheme, termed interference-free orthogonal frequency division multiplexing (IF-OFDM) . Besides, when a transmitter is able to acquire CSIT from its paired receiver only, i.e., local CSIT, a higher sum-spectral efficiency can be achieved by a two-stage transmission method that concatenates IF-OFDM and vector coding based on singular value decomposition with a water-filling power allocation. A major implication of the derived results is that separate encoding across subcarriers per link is sufficient to linearly increase the sum-spectral efficiency with $K$ in the interference channel with ISI. Furthermore, we discuss several key ideas to facilitate the proposed IF-OFDM from a practical perspective even when the desired links do not have sufficiently long impulse responses. Various numerical results are also provided to support this theoretical analysis.