[@wang_liu] for shortening and in [@short_mat; @Chandesris_ICC17] for puncturing. The latency increase due to on-the-fly reliability calculation brought 3GPP to prefer an alternative approach, namely to design the matching pattern on the basis of the frozen set [@isit_punc; @ARQ_punct]. This significantly reduces the code design complexity, albeit at the cost of an increased block error rate (BLER). The joint optimization of frozen set and matching pattern, as proposed in [@short_milo], has been evaluated too, however it has been discarded due to its excessive complexity.

When the code length $E$ is slightly larger than a power of two, a large number of bits would not be transmitted if puncturing or shortening were to be applied, since the mother polar code length would have to be selected as the successive power of two. In this case, extending a smaller polar code, i.e. retransmitting some code bits, may be preferable in terms of decoding latency and error correction performance [@ARQ_polar] since a smaller mother polar code decoder can be used combining the likelihoods of retransmitted bits. The presence of repeated code bits due to retransmission alters the bit-channels reliability, however without giving restrictions to code design as for puncturing or shortening [@ARQ_punct]. This 