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

Abstract: We consider a two-user Gaussian interference channel with heterogeneous blocklength constraints (HB-GIC), strong interference, and two private messages. We propose to apply the successive interference cancellation with early decoding, i.e., decoding a message with a number of received symbols less than the blocklength at the receiver. We determine the necessary number of received symbols to achieve successful decoding of the longer codeword that satisfies the input power constraints and target average error probability constraints. To attain the results, we investigate the dependence testing bound analysis over an independent and identically distributed (i.i.d.) Gaussian input. Besides, we derive the second-order achievable rate region of the considered HB-GIC. By numerical results based on the rate-profile approach, we compare the derived second-order rate region to the first-order one, which shows the rate back-off of the considered model due to the impact of finite blocklength.