Sequence-Selection-Based Constellation Shaping for Nonlinear Channels

TL;DR

This work investigates probabilistic constellation shaping (PCS) for nonlinear optical channels by introducing and evaluating sequence selection as a nonlinear shaping mechanism. It shows that ideal sequence selection can provide up to $0.13$ bit/s/Hz gain over optimized PAS when the selection metric accounts for symbol signs, while practical implementations (notably FEC-independent bit scrambling) can reach about $0.08$ bit/s/Hz gains, with complexity and metric evaluation as primary challenges. The study demonstrates that signs must be incorporated in the selection metric, and that gains persist under carrier phase recovery (CPR). Moreover, sequence selection exhibits robustness to changes in symbol rate and link length, offering flexible gains across a range of WDM configurations. Overall, sequence selection emerges as a viable route to nonlinear shaping, enabling marginal yet meaningful improvements in spectral efficiency in realistic systems when paired with appropriate FEC and CPR considerations.

Abstract

Probabilistic shaping is a pragmatic approach to improve the performance of coherent optical fiber communication systems. In the nonlinear regime, the advantages offered by probabilistic shaping might increase thanks to the opportunity to obtain an additional nonlinear shaping gain. Unfortunately, the optimization of conventional shaping techniques, such as probabilistic amplitude shaping (PAS), yields a relevant nonlinear shaping gain only in scenarios of limited practical interest. In this manuscript we use sequence selection to investigate the potential, opportunities, and challenges offered by probabilistic shaping for nonlinear channels. First, we show that ideal sequence selection is able to provide up to 0.13 bit/s/Hz gain with respect to PAS with an optimized blocklength. However, this additional gain is obtained only if the selection metric accounts for the signs of the symbols: they must be known to compute the selection metric, but there is no need to shape them. Furthermore, we show that the selection depends in a non-critical way on the symbol rate and link length: the sequences selected for a certain scenario still provide a relevant gain if these are modified. Then, we analyze and compare several practical implementations of sequence selection by taking into account interaction with forward error correction (FEC) and complexity. Overall, the single block and the multi block FEC-independent bit scrambling are the best options, with a gain up to 0.08 bit/s/Hz. The main challenge and limitation to their practical implementation remains the evaluation of the metric, whose complexity is currently too high. Finally, we show that the nonlinear shaping gain provided by sequence selection persists when carrier phase recovery is included.

Figures (13)

• Figure 1: Rate loss versus block length.
• Figure 2: SE versus power with conventional DMs.
• Figure 3: Sequence selection.
• Figure 4: Optimal SE versus acceptance rate $\eta$ with ideal sequence selection with (a) shaped signs (solid) and unshaped unknown signs (dashed), and (b) shaped signs (solid) and unshaped known signs (dotted).
• Figure 5: Performance with sequence selection (with shaped signs and SpSh as unbiased source) versus number of spans $N_{\text{span}}$ when the sequences are selected for $N_{\text{span}}=30$ with dashed lines (a) SE, and (b) SNR gain, compared with performance when sequences are selected for the actual $N_{\text{span}}$ with solid lines.