A 5G new radio cellular system is characterized by three main usage scenarios of enhanced mobile broadband (eMBB), ultra-reliable and low latency communications (URLLC), and massive machine type communications, which require improved throughput, latency, and reliability compared with a 4G system. This overview paper discusses key characteristics of 5G channel coding schemes which are mainly designed for the eMBB scenario as well as for partial support of the URLLC scenario focusing on low latency. Two capacity-achieving channel coding schemes of low-density parity-check (LDPC) codes and polar codes have been adopted for 5G where the former is for user data and the latter is for control information. As a coding scheme for data, 5G LDPC codes are designed to support high throughput, a variable code rate and length and hybrid automatic repeat request in addition to good error correcting capability. 5G polar codes, as a coding scheme for control, are designed to perform well with short block length while addressing a latency issue of successive cancellation decoding.

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A design of rate-compatible polar codes suitable for HARQ communications is proposed in this paper. An important feature of the proposed design is that the puncturing order is chosen with low complexity on a base code of short length, which is then further polarized to the desired length. A practical ratematching system that has the flexibility to choose any desired rate through puncturing or repetition while preserving the polarization is suggested. The proposed rate-matching system is combined with channel interleaving and a bit-mapping procedure that preserves the polarization of the rate-compatible polar code family over bit-interleaved coded modulation systems. Simulation results on AWGN and fast fading channels with different modulation orders show the robustness of the proposed ratecompatible polar code in both Chase combining and incremental redundancy HARQ communications.

A design of rate-compatible polar codes suitable for HARQ communications is proposed in this paper. An important feature of the proposed design is that the puncturing order is chosen with low complexity on a base code of short length, which is then further polarized to the desired length. A practical ratematching system that has the flexibility to choose any desired rate through puncturing or repetition while preserving the polarization is suggested. The proposed rate-matching system is combined with channel interleaving and a bit-mapping procedure that preserves the polarization of the rate-compatible polar code family over bit-interleaved coded modulation systems. Simulation results on AWGN and fast fading channels with different modulation orders show the robustness of the proposed ratecompatible polar code in both Chase combining and incremental redundancy HARQ communications.

A practical rate-matching system for constructing rate-compatible polar codes is proposed. The proposed polar code circular buffer rate-matching is suitable for transmissions on communication channels that support hybrid automatic repeat request (HARQ) communications, as well as for flexible resourceelement rate-matching on single transmission channels. Our proposed circular buffer rate matching scheme also incorporates a bit-mapping scheme for transmission on bit-interleaved coded modulation (BICM) channels using higher order modulations. An interleaver is derived from a puncturing order obtained with a low complexity progressive puncturing search algorithm on a base code of short length, and has the flexibility to achieve any desired rate at the desired code length, through puncturing or repetition. The rate-matching scheme is implied by a two-stage polarization, for transmission at any desired code length, code rate, and modulation order, and is shown to achieve the symmetric capacity of BICM channels. Numerical results on AWGN and fast fading channels show that the rate-matched polar codes have a competitive performance when compared to the spatially-coupled quasi-cyclic LDPC codes or LTE turbo codes, while having similar rate-dematching storage and computational complexities.