  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.
