Long Codewords: The Secret to Successful Probabilistic Constellation Shaping

Probabilistic constellation shaping (PCS): it’s the next big thing in high-performance coherent transmission.  The promise of PCS is that it will allow a given transponder to deliver a combination of wavelength data rate and optical reach that is close to the theoretical capacity limit of the cable (aka the Shannon limit).

Let me give you a brief reminder of how probabilistic constellation shaping works, and then I’ll explain one of the most important features to look for in an effective PCS implementation: long codewords.

As you increase the modulation order from, for example, QPSK right up to 64QAM, the optical reach drops exponentially while the spectral efficiency rises quite modestly.  But operating with the highest modulation you can use for a given reach is a vital way to lower cost per bit in the network and maximize fiber capacity, so it’s a good part of network design to maximize modulation order. PCS addresses this problem.

If we use discrete modulation, the result is shown in Figure 1 – there is a “sawtooth” effect as the transponder switches from one modulation to another.  Figure 1 also shows a dotted line representing the Shannon limit – if you are operating the link close to one of the drops in the sawtooth, the effect is that you are further away from the Shannon limit.

Figure 2 shows that PCS starts with a full 64QAM constellation, and I’m showing only one polarization for simplicity.  Over short distances we can use the full constellation, and a PM-64QAM symbol will carry 12 bits of data.

However, as reach increases, the outer symbol locations of these constellations are the most challenging for a receiver to detect reliably, so what PCS does is reduce the probability of these outer symbols being used to encode data, and increase the probability of the inner symbols being used.  On the right of Figure 2, you can see a 3D probability map, where the ideal shape follows a Gaussian distribution.

A key point is that these probabilities can be changed much more smoothly than switching between hard modulations and, in Figure 1, the result will be to smooth out the sawtooth shape of the curve.  Note that there will still be a sawtooth, but it will be much finer because its granularity is now determined by the need to map discrete client data rates into the wavelength.

The side effect of this probability manipulation is that there will be fewer bits per symbol available into which the transponder can map the data stream.

What Is a PCS Codeword Anyway?

PCS implementations include a mapping algorithm that will try to ensure that the most bits per symbol are available for a given optical performance level.  This mapping is more efficient the further the algorithm can look into the upcoming data stream.

The analogy I would use is a chess program.  According to Wikipedia, most chess software developers agree that looking at least five moves ahead is necessary to play well.  But on average, there are more than 30 legal chess moves from any given position, so a computer that is looking five moves ahead would have to examine a quadrillion possible moves!  Chess software uses clever techniques to prune this number drastically, but the basic principle holds true.

Some vendors have already announced PCS implementations with rather short codeword lengths, but what does that mean in practice?  Since the PCS algorithm does not have the chance to look deep into the data stream, there is a higher probability that it will be forced to map a particular set of bits onto one of the outer symbols in the constellation, which would reduce the reach for those bits, as well for as any other bits that suffer a similar fate.

In our initial analysis of PCS, we quickly identified the importance of codeword length. Figure 3 shows the PCS benefit to signal-to-noise ratio tolerance expressed as a function of the codeword length. Armed with this result, we drove toward an implementation that delivers essentially all potential benefit. For competing solutions, we see that they have imposed constraints on the codeword length, which means that almost half of the benefit is lost.

Initially we were concerned that choosing a longer codeword would have a big impact on implementation complexity and power dissipation. Fortunately, we were able to optimize this complicated algorithm such that overall power dissipation within the key PCS blocks of our sixth-generation Infinite Capacity Engine (ICE6) optical engine is a tiny fraction of total power.  And, in case you were wondering, extending the codeword length has no noticeable effect on latency, which is a real win-win.

So, when it comes to selecting a truly industry-leading PCS, don’t forget to ask…how long is your codeword?