This page builds every word, symbol, and picture the parent note leans on. Read it top to bottom — nothing below uses anything not defined above it. When you can pass the #Equipment checklist at the bottom, go read the main topic note.
Picture a single wire. If we agree that "low voltage = 0" and "high voltage = 1", then by watching the wire's voltage over time we can read a stream of bits.
Look at the blue line in the figure: each flat section is one bit-slot. Where the line is low it means 0, where it is high it means 1. Reading left to right gives 0 1 1 0 1. The width of each slot is the bit period — how long each bit is "held" on the wire.
Why a new word "transfer" instead of just "bits"? Because — as we'll see in Section 6 — not every slot on the wire carries a useful data bit; some slots are used for housekeeping. "GT/s" honestly counts slots on the wire; the useful-data rate is always a bit lower.
For the older encodings, useful bits per transfer =1, so 8 GT/s ≈ 8 Gb/s of raw line rate.
A single wire near motors, radios, and other chips picks up stray voltage — electromagnetic interference (EMI) — random voltage bumps that can flip a 0 into a 1.
The fix is to send the signal on two wires at once: one carries the signal, the other carries its exact mirror image. The receiver looks only at the difference between them.
In the figure, the orange and green lines are the two wires; when noise hits (the gray wobble) it lands on both equally, so it cancels when you subtract them. The blue line at the bottom is that clean difference. This is called differential signalling, and the two wires are a differential pair.
The figure shows one lane: the orange TX pair leaves the chip, the green RX pair arrives, and both are busy at the same instant. The parent note's "2R" for a lane comes straight from here — rate R going out plus rate R coming in.
Why "x16" and not "x32"? x16 is the widest link ever actually built; more lanes cost too many pins and traces to be worth it.
Now the tricky part. To read the wire correctly, the receiver must know exactly where each bit-slot starts. It figures this out by watching for voltage flips. But if the data is a long run of identical bits (say 0000000000), the wire never flips and the receiver loses its place — like counting fence-posts in fog.
Two schemes appear in the topic:
8b/10b: take 8 real data bits, send 10 bits on the wire. 2 of every 10 bits are "overhead" (housekeeping, not data).
128b/130b: take 128 real data bits, send 130 on the wire. Only 2 extra per 128.
The parent note uses a handful of pure-maths tools. Here is each, from zero.
Why log2 and not ordinary division? Because information doubles every time you add one bit, and log2 is exactly the tool that "undoes" doubling — it converts number of choices into number of bits.
Why a polynomial and not plain numbers? Because "divide and keep the remainder" catches accidental bit-flips extremely reliably, and polynomials-over-bits make that division cheap in hardware.
