In this paper, we resort to results presented in the Costa's paper [1], and employ LDPC (low-density parity-check) codes to investigate the achievable sum-rates for the Gaussian Interference Channel (GIC). We assume a symmetric GIC and the same power for both users. A different decoding scheme is employed for each interference region. For the weak interference region, user's interference is treated as noise. For the moderate interference region, we use nonnaive time division multiplexing (TDM) approach. For the strong interference region, joint decoding is employed and finally, for the very strong interference region, the SIC (successive interference cancellation) method is used. Numerical simulations have been performed to show that the gap between the Han and Kobayashi limit and the achievable sum-rate is very small.