Kurtosis-Limited Sphere Shaping for Nonlinear Interference Noise Reduction in Optical Channels

Abstract

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Band-ESS: Streaming Enumerative Coding with Applications to Probabilistic Shaping

“…In the inset of Fig. 4, we show the maximum ρ that satisfies (5) when used in (13) to compute the trellis for the set of parameters given in Example 1. We also show the behavior when 𝑁 and 𝐿 are increased to 256 and 257, resp.…”

“…However, via proper modifications in the ESS algorithm, other types of signal space constructions and input distributions can be obtained. For instance, we have recently introduced kurtosis-limited ESS (K-ESS) [13] which introduces a constraint on the maximum fourth power of the norm of amplitude sequences (i.e., kurtosis) in addition to the sphere constraint on their squared norm (i.e., energy) and hence, achieves Gaussian-like input distributions with smaller kurtosis. Such distributions provide higher achievable rates than MB distributions for short-haul optical links [14], [15] and thus, K-ESS has been shown to provide SNR gains and reach increases over ESS.…”

Probabilistic Amplitude Shaping and Nonlinearity Tolerance: Analysis and Sequence Selection Method

“…The parameters for the two simulation setups are adopted from [18] and [21] and shown in Tables I and II, respectively. a) Setup 1 [18]: A multi-span WDM transmission with 11 channels, 32 GBd baud rate, and 50 GHz channel spacing is simulated using the SSFM.…”

“…b) Setup 2 [21]: The main differences from Setup 1 are the adoption of 64 QAM transmission, PAS with ESS and K-ESS with a shaping rate of 1.5 bits/amplitude and a rate-5/6 FEC, i.e., the overall rate is 4 bit/QAM-symbol, a baud rate of 50 GBd, a channel spacing of 55 GHz for the WDM case, and a single-span link of 205 km. The other parameters are identical or similar (see Tables I and II).…”

“…For example, the trellis of the enumerative sphere shaping (ESS) algorithm [20] can be adjusted to obtain sequences with improved nonlinearity tolerance. This has been done based on the per-sequence kurtosis in K-ESS [21] and considering sequence-energy variations in band-trellis ESS (B-ESS) [22]. The bisection-based implementation of CCDM (BS-CCDM) presented in [23] exploits the redundancy in CCDM to remove unfavorable CCDM sequences and thus mitigate fiber nonlinearity.…”