Squeezing out the last few bits from band-limited channels with entropy loading

The past decade witnessed the stirring development of advanced optical modulations and digital signal processing, which have been pushing optical transmission systems towards the capacity limit. Recent research has sought to squeeze out the last few bits from bandwidth-limited optical channels. One straightforward path is to expand the signal spectrum beyond the bandwidth limit while keeping the single-carrier modulation, which inevitably induces huge inter-symbol interference. To cope with such penalty, sophisticated digital nonlinear equalization on single-carrier signals should be exploited to reduce the burden of the subsequent forward error corrections (FEC). On the other hand, a more instinctive capacity-approaching method for bandwidth-deficient channels is the well-known water-filling realized by multicarrier modulation. As its approximation, bit loading (BL) has been a well-established algorithm to maximize the bit rate of a discrete multitone (DMT) channel with fixed-rate FEC. Built on probabilistic constellation shaping (PCS), multicarrier entropy loading (EL) goes beyond BL by continuous source entropy adaptation and has proven its superiority over the single-carrier PCS counterpart. In this paper, we reveal the EL advantage over BL on both achievable information rate (AIR) and FEC, aiming to prove EL as the optimum capacity-approaching solution for bandwidth-limited channels with frequency-selective fading. In a 100G direct detection system with a bandwidth-deficient directly modulated laser, EL improves the AIR by 5%-10% over BL using identical FEC overhead. EL will be critical for short-reach interconnects dominated by low-cost optical components to squeeze out the last few bits from the bandwidth-constrained system.