This paper deals with two main issues regarding the short polar codes: the potential of FEC-assisted decoding and optimal code concatenation strategies under various design scenarios. Code concatenation and FEC-assisted decoding are presented systematically, assuming a packetized system. It is shown that FEC-assisted decoding can improve frame error rate of successive cancellation decoding arbitrarily, at the expense of some coding rate loss and decoding complexity linearly increasing with the number of codewords in the frame. This is compared with list decoding whose complexity grows linearly with the list size as well as the number of codewords. Thereafter, the frame construction procedure and decoding algorithm are developed in a realistic framework. Taking into consideration the effective throughput of the transmission protocol, the problem of optimal design of concatenated codes is formulated under polar code length, frame length and target frame-success-rate constraints. Simulations are performed assuming both additive white Gaussian noise and Rayleigh fading channels. It is shown that the divide-concatenate strategy for long frames does not lead to any considerable gain. It is also shown that the performance of FEC-assisted decoding of frames is improved as the frame length increases while the conventional successive cancellation decoding undergoes a dramatic performance loss.