This paper compares the turbo code and rate-compatible low-density parity-check (LDPC) codes based on the block error rate (BLER) performance and decoding complexity in order to clarify which channel coding scheme is most appropriate for the channel coding scheme in the OFDM based Evolved UTRA (E-UTRA) downlink. Simulation results and the decoding complexity analysis show that although the Rate-Compatible/Quasi-Cyclic (RC/QC)-LDPC code employing an offset layered belief propagation (BP) method can reduce the computational complexity by approximately 30% for the channel coding rate of R ≥ 1/2, the required average received signal energy per bit-to-noise power spectrum density ratio (E_b/N₀) is degraded by approximately 0.2-0.3dB for R=1/3, 1/2 and 3/4 compared to that for the turbo code. Moreover, the decoding complexity level of the RC/QC-LDPC code with the δ-min algorithm is almost the same or higher than that for the turbo code with a slight degradation in the required received E_b/N₀. Although the decoding complexity level of the ZigZag code is lower than that of the turbo code, the code brings about a distinct loss in the required average received E_b/N₀ of approximately 0.4dB. Finally, the turbo Single Parity Check (SPC) code improves the BLER performance compared to the ZigZag code, i.e., achieves almost the same BLER performance as that for the turbo code, at the cost of a two-fold increase in the decoding complexity. As a result, we conclude that the turbo code with a contention free interleaver is more promising than the LDPC codes for prioritizing the achievable performance over complexity and as the channel coding scheme for the shared data channel in the E-UTRA.