Part II Selected Topics
8.5 Link Characteristics
The wealth of possibilities for communication modes is challenging and inspiring.
At the same time, when we want to design specific systems, it is useful to have ways to compare different possible choices. The question of cost is of course always an overarching one. The next question then is how to quantify what is being commu- nicated so that we can compare costs between solutions of similar or comparable performance.
In general, the performance of a communication link is not quantified as a single quantity, but rather, as a composite of different characteristics. Commonly considered characteristics are latency, bandwidth, and various notions of reliability. While ice- cream, of course, is not the only means of communication, it can illustrate some common physical characteristics of links. In the context of cyber-physical systems, the mobility of the communicating entities makes the situation more interesting, as
136 8 Communications all of these characteristics can depend on both the relative location of the entities as well as their environment.
8.5.1 Latency
Latency is the time it takes from sending a signal to receiving it. If we imagine that the two people are 50 cm apart and the ice-cream can be moved at a speed of 1 m/s, then it will take 0.5 s to transmit the ice-cream. While for interpersonal communication such delays may be acceptable, for applications such communicating a signal from car brake pedals to wheels, much shorter delays are required.
Clearly, faster transport speeds can lead to shorter latencies. This is an important reason why media such as electric current and electromagnetic waves (light and radio) are popular. Light can move much faster than our ice-cream in this example, in fact, almost 300 million times faster. But we should keep in mind that for any non-zero distance and finite speed, transmission over this distance will experience non-zero delay.
Physics limits the minimum latency more than we may realize at first. In particu- lar, the theory of special relativity suggests that not only is there always a non-zero delay, but there may be an absolute, minimum delay between two objects with a non-zero distance between them. In particular, the theory suggests that it is impos- sible to travel faster than the speed of light. This means that the shortest time any transmission can take between the two people in our ice-cream example is about 1.67 ns (nanoseconds). Another way of looking at this is that no signal can travel more than about 30 cm in a nanosecond. This constraint is significant in large-scale systems such as communication via satellites or when communicating with someone on the moon. Light takes about 1.3 s to travel between Earth and the moon.
As an aside, for a historic illustration of the significance of understanding these basic constraints, and if you have not done so already, we recommend that you find and watch the two-minute YouTube video entitled “Admiral Grace Hopper Explains the Nanosecond.”
8.5.2 Bandwidth
Bandwidth is the number of messages that can be sent per unit time. Note that this notion cannot be meaningful unless messages can only be split into a finite number of indivisible messages. Thus, the notion of bandwidth requires that messages are discrete entities. For uniformity, a message can be taken to be one of exactly two possible values, that is, one bit. Note also that bandwidth is based on the data being transmitted rather than the information it conveys, as the latter is always a function of the beliefs of the receiver.
Considering our example above, if we assume that there are no verbal or visual hints given by the first person, the “message” can be seen as being one of two things:
Either one ice-cream is handed over, or none are. If we further consider that this event can occur only once per day, then the maximum transfer rate is one message per day. Since there are only two possible events, let us consider the message to be one bit.
Assuming that the information the receiver takes from getting the ice-cream is that the sender likes them, this is a like/neutral signal. If the sender and/or the receiver would like more detailed information, such as really-like/like/neutral, then more bandwidth would be needed. This can be achieved, for example, through the use of two ice-creams. So that the information mentioned can be represented by two-ice- creams/one-ice-cream/no-ice-cream. Of course, such transmissions may cost more or require more work, but the amount of information that can be transmitted increases.
As we will often see, physical resources can often limit the rate of transfer. For example, there is only so many standard sized ice-cream cones and scoops on the planet. But what is physically transmitted is only one source of limitation. In the following exercise, we consider some others.
Exercise 8.5In the above example, using twice as many ice-creams did not double the levels of “like” that we have.
1. Are there ways in which a maximum of two ice-creams per day can be used to communicate four like levels, such as like-a-lot/like/like-a-bit/neutral?
2. What is the key idea that you are using to achieve this higher level of information transfer? In other words, is there a reason why this method can be expected to generalize to other situations?
8.5.3 Reliability
Under idealized conditions, for example, the universe consists only of you, your friend, and the ice-cream, the transmission of the ice-cream should be quite reliable:
Once you start the process of handing over the ice-cream to your friend, the expected outcome for them should be that they receive it and recognize the message. But idealized conditions may be hard or even too difficult to provide. Instead, you and your friend could be standing outdoors on a windy day, they may be looking the other way as you get the ice-cream that you wish to give to them, and a wind might come and blow away the ice-cream before you are able to offer it to your friend.
Alas, the physical evidence of the ice-cream is now gone. This kind of situation is a simplified example of the reliability issues that arise in almost all real-world communications. In general, they can also become more challenging as we try to transmit more information, over larger distances, in dynamic environments, and between mobile entities.
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