Modulated coded zero-forcing decision feedback equalizer

Modulated codes (MC) are error correction codes (ECC) over the real/complex field, which are used for mitigating the intersymbol interference (ISI). The arithmetic operations of the MC encoder are the same as the ones of an ISI channel, therefore, an ISI channel and an MC can be naturally combined together. With the combination, the MC can be optimally designed for the mitigation of the ISI. In this paper, we propose a new coded zero-forcing decision feedback equalizer (ZF-DFE) using MC. For the MC coded ZF-DFE we present the performance analysis and the optimal MC design for a given ISI channel, where the coding gain based on the joint ZF-DFE is formulated comparing to the uncoded AWGN channel. Our numerical results show that the MC coded ZF-DFE outperforms the conventional uncoded/coded ZF-DFE and the uncoded/coded Tomlinson-Harashima (TH) precoding at, at least, low channel SNR, where the BPSK is used.