The coding technique that combines channel estimation and error correction has received attention recently, and has been regarded as a promising approach to counter the effects of multipath fading. It has been shown by simulation that a proper code design that jointly considers channel estimation can improve the system performance subject to a fixed code rate as compared to a conventional system which performs channel estimation and error correction separately. Nevertheless, the major obstacle that prevents the practice of such coding technique is that the existing codes are mostly searched by computers, and subsequently exhibit no apparent structure for efficient decoding. Hence, the operation-intensive exhaustive search becomes the only decoding option, and the decoding complexity increases dramatically with codeword length. In this paper, a systematic construction is derived for a class of structured codes that support joint channel estimation and error correction. It is confirmed by simulation that these codes have comparable performance to the best simulated-annealing-based computer-searched codes. Moreover, the systematically constructed codes can now be maximum-likelihoodly decoded with respect to the unknown-channel criterion in terms of a newly derived recursive metric for use by the priority-first search decoding algorithm. Thus, the decoding complexity is significantly reduced as compared with that of an exhaustive decoder.