Frequency-modulated differential chaos shift keying (FM-DCSK) is an attractive scheme which combines chaotic modulation with the spread-spectrum property. It is simple to implement and robust in multipath fading channels. A single-input multiple-output (SIMO) FM-DCSK architecture has recently been developed to increase data rate and achieve diversity gain. In this paper, several main channel coding schemes, i.e., error-correcting coding schemes, are introduced into the SIMO FM-DCSK communication system, with different code rates and different frame lengths, over multipath fading channels. It is found that, in contrast to low density parity check codes and convolutional codes, product accumulate (PA) codes can provide outstanding bit error rate performance improvement to the existing SIMO FM-DCSK system. In this paper, moreover, the optimum code rate for the PA-coded SIMO FM-DCSK system is investigated through simulations at a medium frame length. Because of its merits in several aspects, such as prominent advantages in better performance, simple encoding and decoding structures, and a flexibly adjustable code rate, this paper demonstrates that PA code is a strong candidate as the error-correcting scheme for the SIMO FM-DCSK system in transmitting medium and long frame lengths over multipath fading channels.