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PROFESSOR: Today we finish up chapter 13. I think we are finished, but I'll take questions. We get into chapter 14, which starts to get into coding for bandwidth-limited channels. Here we're coding directly in terms of Euclidean space rather than in terms of Hamming space. And there's this wonderful quote from Neil Sloane. "Euclidean space coding is to Hamming space coding as classical music is to rock'n'roll." Meaning that, in the Euclidean space, things are continuous, whereas we were discrete back in Hamming space. Nonetheless, there are strong connections between the two, which in two lectures I'll basically only have a chance to hint at. You were supposed to hand in problem set nine last Friday, or today if you haven't already. Today, we'll hand out the solutions for nine, and then chapter 14 and its problems, which are problem set 10. These are not due. As always, I recommend you do them. The solutions will be handed out Wed...

We're going to pick up where we left off on Monday. And where we left off was we were dissolving stuff. We talked about how things dissolve. Why does something dissolve maybe in this solvent versus that? And how does it dissolve? And what makes them-- and then we say, well, what if we had something and we wanted it to dissolve all the way until it couldn't dissolve anymore? Well, that's called saturation, right? And we talked about that. We talked about how if you had a general reaction, maybe we had something like this, aA plus bB goes to and comes back from cC plus dD, then this reaction can happen in both ways, right? And so the general concept that we called a reaction quotient, reaction Q, is equal to-- remember, it's equal to the concentrations raised to those stoichiometric coefficients. And it's the products over the reactants. OK, so that's what we-- now then, we say, well OK, that's a thing that has to do with maybe-- where's that...

Let's wrap up our discussion of system-level interconnect by considering how best to connect N components that need to send messages to one another, e.g., CPUs on a multicore chip. Today such chips have a handful of cores, but soon they may have 100s or 1000s of cores. We'll build our communications network using point-to-point links. In our analysis, each point-to-point link is counted at a cost of 1 hardware unit. Sending a message across a link requires one time unit. And we'll assume that different links can operate in parallel, so more links will mean more message traffic. We'll do an asymptotic analysis of the throughput (total messages per unit time), latency (worst-case time to deliver a single message), and hardware cost. In other words, we'll make a rough estimate how these quantities change as N grows. Note that in general the throughput and hardware cost are proportional to the number of point-to-point links. Our baseline is the backplane b...

Let's finish up by looking at two extended examples. The scenario for both examples is the control system for the International Space Station, which has to handle three recurring tasks: supply ship guidance (SSG), gyroscope control (G), and cabin pressure (CP). For each device, the table shows us the time between successive requests (the period), the service time for each request, and the service deadline for each request. We'll first analyze the system assuming that it's using a weak priority system. First question: What is the maximum service time for the cabin pressure task that still allows all constraints to be met? Well, the SSG task has a maximum allowable latency of 20 ms, i.e., it's service routine must start execution within 20 ms if it is to meet its 25 ms deadline. The G task has a maximum allowable latency of 10 ms if it's to meet its deadline. So no other handler can take longer than 10 ms to run or the G task will miss its deadline. 2. G...