Exponents of Hybrid Multi-Kernel Polar Codes
Lei Cheng, Lijun Zhang, Qiang Sun · 2018
Multi-kernel polar codes are constructed from the Kronecker product. For ordinary multi-kernels, constituent polarizing matrices of the same stage are identical. However, in a stage, applying different constituent matrices based on channel property can further improve performance. This family of polar codes is defined as hybrid multi-kernel polar codes. Exponents of hybrid multi-kernels are analyzed. The matrix of a hybrid multi-kernel is generated by a Kronecker-like product operation, and so are partial distances. All exponents of hybrid multi-kernels take values between the maximum and the minimum exponents among all constituent matrices. Exponents are related to the error probability of the original channel and exhibit a trend of convergence as block-length increases. The convergence rate is also related to the original error probability.