Theoretical analysis of achievable rates for channel-polarized multilevel coding under binary-input AWGN channels

High-performance and low-complexity forward error correction (FEC) has attracted attention in high-speed optical-fiber communications to reduce the power consumption of digital signal processors (DSPs) for digital coherent systems. Multilevel coding (MLC) provides a solution to reduce the decoding complexity by utilizing soft-decision decoding (SDD) only in low-capacity bit-levels on symbols. However, the amount of reduction for MLC with low-modulation order is lower than the high modulation order because of the large ratio of the least significant bit to the entire code frame. Channel-polarized MLC (CP-MLC) has been reported, which is binary MLC that applies SDD to only a low-capacity channel converted by channel-polarization. Reported simulation results show that CP-MLC can reduce the decoding complexity while mitigating performance degradation. To efficiently implement CP-MLC into the DSPs, theoretical analysis is necessary for the optimal design of CP-MLC. This paper derives and analyzes the CP-MLC capacity, which is the maximum achievable rate, under a binary-input additive white Gaussian noise (BAWGN) channel to determine the decoding performance limit for each ratio of SDD to hard-decision decoding (HDD). Our results show that CP-MLC can provide better upper bounds of performance than HDD and reduce the decoding complexity by decreasing the SDD ratio while mitigating the performance gap with the capacity of the BAWGN channel. We also demonstrate that the theoretical analysis can estimate the performance of CP-MLC applied to practical codes.