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We consider a two-user Gaussian interference channel with heterogeneousblocklength constraints (HB-GIC), strong interference, and two privatemessages. We propose to apply the successive interference cancellation withearly decoding, i.e., decoding a message with a number of received symbols lessthan the blocklength at the receiver. We determine the necessary number ofreceived symbols to achieve successful decoding of the longer codeword thatsatisfies the input power constraints and target average error probabilityconstraints.  To attain the results, we investigate the dependence testing bound analysisover an independent and identically distributed (i.i.d.) Gaussian input.  Besides, we derive the second-order achievable rate region of the consideredHB-GIC. By numerical results based on the rate-profile approach, we compare thederived second-order rate region to the first-order one, which shows the rateback-off of the considered model due to the impact of finite blocklength.

Second-order Rate Analysis of a Two-user Gaussian Interference Channel with Heterogeneous Blocklength Constraints