Baud Rates and 800 Gb/s: Every Little Bit Helps (A Lot)
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Baud Rates and 800 Gb/s: Every Little Bit Helps (A Lot)

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July 22, 2021
By Paul Momtahan
Director, Solutions Marketing

Yesterday I presented a Lightwave webinar on the What, How, and Why of 800G Generation Optical Engine Performance, where I attempted to explain the key factors that drive 800G performance. One surprising factor relates to the relationship between baud rate and wavelength capacity-reach at different data rates.

This reminds me of the expression “every little bit helps,” often shortened to “every little helps,” which is also the long-standing advertising slogan for British supermarket retailer Tesco, and means that “even the smallest things are helpful when towards a goal.” It turns out that with ultra-high data rate (i.e., 800 Gb/s) wavelengths, the same adage applies equally to the baud rate, with a relatively small increase in the baud rate leading to a potentially disproportionate increase in the reach.

Let me explain.

High Baud Rates and Capacity-Reach

As outlined in an earlier blog, “Coherent Baud Rates: Is Higher Always Better?” and described in more detail in the Infinera white paper “Baud Rate, Modulation, and Maximizing Coherent Optical Performance,” higher baud rates provide the key lever for increasing wavelength capacity-reach. Higher baud rates enable the use of lower-order modulation to achieve the same data rate. Lower-order modulation benefits from greater Euclidean distance between constellation points, making them easier to distinguish in the presence of noise.

At the same time, as the spectrum of the wavelength is proportional to the baud rate, a higher-baud-rate wavelength can leverage higher power for the same power spectral density and therefore the same level of nonlinearities.

Together, lower-order modulation and higher power more than offset the increased sensitivity to noise and nonlinearities of the higher baud rate itself, resulting in significant capacity-reach improvements.

The “1 bit = 3 dB Rule”

A well-known rule of thumb with higher-order modulation and coherent transmission is the “1 bit = 3 dB rule” – doubling the number of constellation points (QPSK → 8QAM, 8QAM → 16QAM) adds one bit per symbol per polarization and approximately halves reach with a 3 dB increase in the required OSNR.

In fact, the Shannon limit itself follows this rule at higher SNR values, where we can ignore the 1 in its famous equation, C/B = Log2 (1+SNR). Adding 1 bit to the spectral efficiency requires us to double (+3 dB) the required SNR, thus halving the reach.

The Modem SNR Limitation

However, as shown in Figure 1, with higher-order modulations (32QAM, 64QAM, etc.), modem SNR, the amount of noise and distortions inside the optical engine, becomes a key limiting factor that further reduces reach. With low-order modulation, the SNR limit is relatively low and optical noise and nonlinearities are the primary limitation on SNR and therefore reach.

With the higher SNR limit of high-order modulation, modem SNR takes up a larger portion of the available noise limit, allowing for a much smaller amount of external noise (i.e., OSNR and nonlinearities).

Figure 1:  Modulation (bits per symbol per polarization) vs. reach

800 Gb/s Reach vs. Baud Rate

Figure 2 shows, for Infinera’s ICE6 optical engine, the relative reach of an 800 Gb/s wavelength with the base baud rate required for 800 Gb/s and the full 64QAM. Increasing the baud rate by around 8% increases the reach by around a factor of three, while increasing the baud rate by around 15% increases the reach by around a factor of four.

These dramatic increases in reach can be explained as follows. As we move away from the full 64QAM, modem SNR becomes less of a limiting factor. Also, with a high number of bits per symbol, increasing the baud rate by 8% reduces the number of bits per symbol per polarization by almost half a bit, while increasing it by 15% reduces the number of bits per symbol per polarization by almost three-quarters of a bit, enabling us to benefit from a large portion of the 1 bit = 3 dB rule. Finally, as we move away from the full 64QAM, we also start to benefit from probabilistic constellation shaping (PCS) gain.

Figure 2: 800 Gb/s wavelengths: ICE6 reach vs. baud rate

At lower data rates, a marginal increase in the baud rate has a less dramatic but still significant impact on the reach: increasing the baud rate by 15% (from the same base as the 800 Gb/s example) increases the 600 Gb/s reach by up to 40% and the 400 Gb/s reach by up to 20%. One reason these increases are less dramatic is because modem SNR is no longer such a key limitation.

A second reason is that the absolute reduction in bits per symbol is proportionally lower, giving us less gain from the 1 bit = 3 dB rule. For example, at 800 Gb/s with the full 64QAM (6 bits per symbol per polarization), a 20% increase in the baud rate reduces the number of bits per symbol per polarization by 1, while at 400 Gb/s (3 bits per symbol per polarization), the same 20% increase in baud rate would reduce the number of bits per symbol per polarization by only half a bit.

A third reason is that at 600 Gb/s and 400 Gb/s, even at the base baud rate, we already benefit from PCS-64QAM gain.

To learn more about this important topic, download the Infinera white paper, “Maximizing the Capacity-Reach of 800G Generation Coherent: Baud Rates, Features, and Modem SNR.”