Think PCS Is All the Same? Think Again.

As described in my earlier blog, “Probabilistic Constellation Shaping: Faster, Further, Smoother,” probabilistic constellation shaping promises to deliver multiple benefits, including enhanced granularity, improved tolerance to noise and/or nonlinearities, and baud rate flexibility. However, the following four factors can determine the gain and benefits of PCS:

Number 1: Codeword Length

Figure 1: The distribution matcher

As described my earlier blog, “Ah, So That’s How Probabilistic Constellation Shaping Works!”, the distribution matcher takes a uniform bit sequence, ones and zeros with equal probability, and converts these into symbols with a desired distribution. How well it does this depends, to a large extent, on how much data it looks at, which we will refer to as the codeword length, shown in Figure 1. A long codeword increases the probability that a good match can be found.

As shown in Figure 2, a codeword length of around 100 symbols results in around half the gain of a codeword with a length of around 1,000 symbols, with diminishing returns as we go much beyond that. A codeword with a little more than 1,000 symbols is therefore enough to deliver almost all the potential gain of PCS. However, in addition to advanced algorithms, long-codeword PCS (LC-PCS) requires an ASIC/DSP with a 7-nm or better process node.

Figure 2: Codeword length vs. PCS gain

Number 2: Transceiver Quality

Another important factor for PCS gain is the quality of the coherent transceiver, the modem signal-to-noise ratio (SNR), which basically describes the amount of noise generated inside the transceiver/modem. Factors that influence the modem SNR include the precision of the DSP; the performance of the digital to-analog converter (DAC), analog-to-digital converter (ADC), Mach- Zehnder modulators, and trans-impedance amplifiers (TIAs); and the quality of the radio frequency (RF) interconnects between the ASIC/DSP and analog electronics (drivers and TIAs) and between the analog electronics and photonics (i.e., the photonic integrated circuit in the case of Infinera’s sixth-generation Infinite Capacity Engine, ICE6). The better the transceiver, the higher the modem SNR. For a practical coherent transceiver, PCS gain is determined by both the codeword length and the modem SNR.

Number 3: The Distribution Shape

Figure 3: Gaussian vs. super-Gaussian

Another factor that can impact PCS performance is the shape of the distribution. For most applications, a Gaussian distribution will deliver the best results.

However, for scenarios where power levels are high and reducing nonlinearities is the priority, such as submarine with uncompensated large effective area fiber, a flatter super-Gaussian distribution, which more evenly spreads the power over the inner constellation points, as shown in Figure 3, can deliver better results.

Number 4: Per-subcarrier PCS with Dynamic Bandwidth Allocation

Figure 4: Wavelengths have higher penalties at the edges

A single-carrier wavelength experiences different penalties across its spectrum, typically with higher penalties toward the edges and lower penalties nearer the center, due to factors such as filter roll-off and DAC/ADC performance, as shown in Figure 4.

Nyquist subcarriers use advanced digital signal processing to divide a single high-baud-rate carrier into multiple lower-baud-rate subcarriers. However, if all the subcarriers must operate at the same data rate, then for a given reach requirement, the capacity will be limited by the outermost subcarriers. Dynamic bandwidth allocation (DBA) enables the data rate on each subcarrier to be set individually with a different bits/symbol setting for PCS.

Figure 5: Uniform subcarriers: limited by outer subcarriers

For example, if all the subcarriers have to be at the same data rate, then for the reach requirement shown in Figure 5, we are limited by the outer subcarriers to 87.5 Gb/s per subcarrier, giving a total of 700 Gb/s for the wavelength. With DBA we can increase the inner subcarriers to 95 Gb/s, 105 Gb/s, and 112.5 Gb/s, increasing the total wavelength capacity to 800 Gb/s, as shown in Figure 6.

Figure 6: Dynamic bandwidth allocation for increased capacity

Alternatively, we could decrease the outer subcarriers to 82.5 Gb/s and 85 Gb/s and increase the inner subcarriers to 90 Gb/s and 92.5 Gb/s to increase the reach with the same wavelength capacity (700 Gb/s), as shown in Figure 7.

Figure 7: Dynamic bandwidth allocation for increased reach

For more information on this important topic, see new the Infinera white paper “Faster, Further, Smoother: The Case for Probabilistic Constellation Shaping.”