Owning to the high peak-to-average power ratio problem, the power efficiency of orthogonal-frequency-divisionmultiplexing (OFDM) systems is usually low. It deteriorates in millimeter wave systems in which the design of an efficient linear power amplifier is much more challenging. The linear-amplification-with-nonlinear-component (LINC) technique can serve as a remedy, decomposing the input signal into two constant-envelop component signals followed by high-efficient nonlinear amplifiers. However, the power combiner, a key component used to combine the amplified signals, is difficult to implement. Combinerless LINC systems employ two transmit antennas such that two component signals can be naturally combined at the receiver. Unfortunately, the performance of combinerless LINC-OFDM systems is seriously degraded if difference, even small, exists between the two channels. The maximum likelihood (ML) receiver can effectively solve the problem; however, its computational complexity is prohibitedly high. We propose a coded combinerless LINC-OFDM system, including a convolutional encoder and a list Viterbi algorithm (LVA) decoder, to solve the problem. The LVA can provide a small number of candidates for the ML detector, dramatically reducing the required computational complexity. We also utilize an enhanced zero-forcing equalizer such that the soft-demapping operation can be effectively conducted. Finally, we propose a simple iterative interference cancellation scheme to further enhance the performance. Simulations show that the proposed combinerless LINC-OFDM system can outperform the conventional OFDM while the consumed power is much lower.