Polar codes have been selected as the channel coding scheme for control channel in the fifth generation (5G) communication system thanks to their capacity achieving characteristics. However, the traditional polar codes support only codes constructed by binary (2x2) kernel which limits the code lengths to powers of 2. Multi-kernel polar codes are proposed to achieve flexible block length. In this paper, the first combinational decoder for multi-kernel polar codes based on successive cancellation algorithm is proposed. The proposed decoder can decode pure-binary and binary-ternary (3x3) mixed polar codes. The architecture is rate-flexible with the capability of online rate assignment and supports any kernel sequences. The FPGA implementation results reveal that for a code of length N = 48, the coded throughput of 812.1 Mbps can be achieved.
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