In parallel interference channels, the sum-rate achieved by joint coding among subchannels can exceed the sum of the achievable rate of each subchannel with individual coding. In this paper, a capacity-achieving joint coding scheme is proposed for parallel symmetric interference channel. First, we provide a motivating example, from which the insights into the joint coding scheme are obtained. Second, we introduce a transmission scheme in two-user parallel symmetric interference channels, where

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... he subchannels can cooperate to cancel interference. Then, by taking advantage of signal level alignment of the interference from different users, we generalize the scheme to multi-user cases. Finally, we prove that our scheme can achieve the sum capacity and illustrate the generalized degrees of freedom gains over individual coding in various interference scenarios.