code of length smaller or equal to 1024: it is in fact possible to extract sub-sequences for shorter codes directly from the universal reliability sequence, hence reducing the sequence storing space. This nested reliability structure represents a real breakthrough in polar code design, and it is probably the most lasting legacy of the standardization process. This impressive result has been achieved by taking into account also distance properties in short polar codes design [@mondelli; @mk_dist_conf], the use of list decoders and the presence of assistant bits in the code [@scal_exp].

SC-based decoding
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Polar codes have been specifically conceived for SC decoding [@arikan], with which they achieve channel capacity at infinite code length. Even if other decoding algorithms like BP [@BP_pc] and SCAN [@SCAN_pc] have been proposed, their poor error correction performance convinced 3GPP to focus the design envisaging an SC-based decoder at the receiver side. In the original formulation of SC, soft information was described in terms of likelihoods [@arikan], that are numerically unstable and not suitable for hardware implementations. This instability has been reduced using log-likelihoods first [@balatsoukas_SCL_HW], and finally eliminated with log-likelihood ratios (LLRs) [@balatsoukas]. The SC algorithm can be implemented in both software and hardware with 