matrix whose size depends on the modulation scheme used [@64QAM], resulting in an increased decoding latency [@PC_CM].

A channel interleaver has been introduced by 3GPP as a low-complexity alternative to PCM; this technique, termed as bit-interleaved polar-coded modulation (BIPCM) [@BIPCM_conf], improves the diversity gain under high-order modulation without increasing the code complexity [@eff_BIPCM]. In BIPCM, the channel is considered as a set of parallel bit channels which can be combined with polar coded bits. Carefully mapping coded bits to modulation symbols offers a certain gain over the conventional random interleaving [@2mary_PCM], which can be further improved designing interleavers adaptive to channel selectivity [@PDM_OFDM]. Finally, the correlation among coded bits mapped into the same symbol allows to combine the demapping and deinterleaving units with the SC decoder to perform the decoding directly on the LLRs of the received symbols [@SC_BIPCM].

Polar Code Encoding in 5G {#sec:5G}
=========================

[.5]{} ![image](figures/UP_plot.pdf){width="95.00000%"}

[.5]{} ![image](figures/DOW_plot.pdf){width="95.00000%"}

In this section we describe in detail the framework adopted for the encoding of polar codes in 5G standard. In the following, the notation introduced in the 3GPP technical specification [@3GPP_R15] will be used. Polar codes are used to encode the uplink control information (UCI) over the physical uplink control 