How Much Data Can Be Pushed Through Copper Wires?

Pushing toward the Shannon signaling capacity using less energy consumption.


As the amount of digital data grows, so do requirements on the speed of the transmission at all levels of the transmission chain—between dies in a shared package, between packaged chips inside a device, and between devices. The communication channels encountered at every stage of this communication are different in nature. Those between dies in a shared package, or between packaged chips in a shared device, are mostly electrical wires. Those between devices can be electrical (as is the case when you connect a laptop to a monitor using a cable), or optical, as is the case when top of the rack switches are connected in a datacenter over longer distances, or even wireless. Each of these channels has its own properties, and communication across them ideally would be orchestrated in such a way as to utilize that channel in the best possible way.

But what is this “best possible way?” In other words, how many bits per second can one transmit on these channels, at least theoretically? An answer to this question will shed some light on how far we are away from these bounds, and how much “air” we still have to breathe.

By far the best answer to this question has been provided by Shannon’s definition of the “channel capacity.” In his seminal 1948 paper he associates with every communication channel a number, called its capacity, and shows that communication on this channel at any rate below this capacity is possible with a residual error that can be made arbitrarily small. At the same time, communication at any rate above the capacity only can be done at the cost of a fixed communication error. Loosely phrased, reliable communication at a given rate is possible if, and only if, that rate is below capacity. Unfortunately, though, Shannon doesn’t tell us how to design efficient communication systems that operate at rates close to the capacity.

Given this fundamental relationship, it seems logical to measure the throughput of any given communication system against the capacity of the underlying channel. This is where we have a huge disconnect between electrical chip-to-chip links, and practically all other important communication channels such as wireless, optical, satellite, DSL, etc.

In all these other communication channels researchers have found ways to come close to the Shannon capacity of the underlying channel. As an example, consider the so-called Additive White Gaussian Noise (AWGN) channel in which transmitted signals are subjected independently to Gaussian noise of mean 0 and variance s2. This is a prototypical channel for wireless communication as results for many other channels can be derived from those for the AWGN channel. If transmitted bits use, on average, a power of P, then the capacity of this communication channel, i.e., the maximum rate at which bits can be transmitted reliably, is B * log2( 1 + P/s2) where B is the bandwidth in Hz.

For chip-to-chip communication, similar formulas can be derived as a function of the underlying channel loss parameters. We are not going to get into the details of these computations, but instead offer an illuminating comparison to wireless channels.

As can be seen, in the wireless world communication rates are quite close to the Shannon capacity of the underlying channel, whereas in chip-to-chip communication over electrical wires the transmission rates are extremely far off. Let’s look at numbers, for example for a channel typically encountered in ultra-short-reach (USR) communication between dies in a shared package. If the SNR (ratio between the average signal power on each wire and the variance of the thermal noise) is 70 dB, then the capacity is about 165 Gbps. How does this compare to today’s communication systems? This SNR corresponds to a peak-to-peak single-ended voltage of 300 mV and a thermal noise standard deviation of 1 mV when using Kandou’s CNRZ-5 Chord Signaling. Kandou’s Glasswing IP achieves approximately 21 Gbps per wire in this generation, and 42 Gbps in the next, while the capacity is 165 Gbps—still away from the capacity, but better than other signaling schemes. For example, for the same power on the wires, differential signaling would have an SNR of 60 dB and a capacity of 124 Gbps, and PAM-4 an SNR of 63 dB and a capacity of 138 Gbps. We are not aware of commercial USR IP’s that use NRZ or PAM-4 at such high speeds.

So why is it that we are still so far off the capacity in chip-to-chip communication? There are several reasons for this. One is that chip-to-chip communication is extremely power-constrained. In fact, the power of signals on the wires is only a small fraction of the total power of the communication system, something that is in stark contrast to systems like wireless. Another reason is the use of ADC’s and advanced DSP algorithms in other communication systems. This is justified because the power used by the ADC and the DSP is miniscule compared to the total power of the system. In chip-to-chip communication this is not the case. Yet another reason is latency. Because of ultra-high speeds in chip-to-chip communication, the tolerated latency is quite small (maybe in the range of a few 100’s of UI). It is difficult to use techniques like strong FEC in such a latency-constrained system.

All of these issues point to the need for radically new techniques that require very little power and yet are capable of approaching the Shannon capacity of the underlying channel. Kandou’s Chord Signaling is one such modulation scheme. In the years to come, Kandou will introduce new methods on top of Chord signaling to increase the throughput with the goal of approaching the Shannon capacity at low energy consumption. The next generation of modulation techniques is already at R&D stage at Kandou and will be introduced to the market in the near future.

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