Six bits in every symbol. That was the summit of the last chapter, and standing on it you can see the obvious next move. The constellation itself is close to full: pack the stars any tighter and the noise starts swallowing them. But nobody said anything about how long a symbol has to last. If every slice of wave carries six bits, deal thinner slices. Flick between stars a million times a second, then ten million. Faster hands, faster internet. Right?
Every radio engineer has stood on this exact ledge and grinned the same grin. So before we start dealing, let's remember something this book taught you back when we were still worrying about walls.
The room talks back#
In chapter 11 you watched a wave meet a slab and suffer one of three fates: pass through, be soaked up, or bounce away. Indoors, bounce wins constantly. Walls, floors, the fridge, a filing cabinet: to a Wi-Fi wave, a room is a hall of dim mirrors. So your signal does not arrive at the receiver once. It arrives, and then it keeps arriving: faint copies of itself that took the scenic route off the far wall or the ceiling, each landing a little late. Radio covers about a foot in a billionth of a second, so a bounce path thirty feet longer shows up thirty billionths of a second behind the direct wave. Chapter 4 named this crowd of copies multipath and showed how it paints dead spots across your kitchen. Now it's about to cause a subtler kind of trouble.
You already know this trouble by ear. Speak in a big stone church and every word comes back off the walls a heartbeat later. Speak slowly and it's lovely: each word's echo dies away inside the word itself, a soft halo around your voice. Now speak fast. Each word's echo is still hanging in the air when the next word begins, syllable landing on syllable, and from ten pews back you are mush.
A symbol stream in a bouncy room is a voice in that church. Below, the blue wave is your signal, flicking from star to star, and under it rides its own echo: the same wave again, fainter and a fixed moment late. Deal slowly and the echo of each symbol fades out harmlessly inside that same long symbol. Now drag the slider and speed up.
the echo stays inside its own symbol: only 17% of each one is smudged
There's the wall we run into, and look closely at what kind of wall it is. The echo arrives just as late no matter how you talk. When symbols are long, that lateness smudges only the opening sliver of each one, and the receiver simply reads the clean part. When symbols are short, the same lateness means each symbol's echo lands squarely on top of the next symbol. The receiver hears now and a-moment-ago at the same time, and no cleverness at the antenna can pull them apart.
And here is the cruel twist: you cannot shout your way out. This isn't the hiss of the noise floor, some outside enemy you can rise above. It is your own signal interfering with itself. Double the transmitter's power and the echo doubles right along with it, arriving just as late and doing just as much damage. Raw symbol speed has a ceiling, and the ceiling is set by the room, not the radio. A bigger antenna, a stronger amplifier, a fancier constellation: none of them move it an inch.
A choir instead of a soloist#
The escape is one of the loveliest ideas in radio, and chapter 16 already handed you the key. A channel, remember, is not a line on the dial but a shelf: a band of frequencies with room for many separate ingredients sitting side by side. So far we've used the whole twenty-megahertz shelf of a Wi-Fi channel to carry one stream. Nothing forces that. Slice the shelf into hundreds of thin sub-lanes instead, park a separate little carrier in each one (a subcarrier), and give every subcarrier its own slow constellation stream.
Now do the arithmetic. Hundreds of lanes, each dealing symbols hundreds of times slower, deliver exactly as many symbols per second as one lane dealing at a sprint. Nothing is lost. But everything is gained, because each symbol in a slow lane is now enormously long. A modern Wi-Fi channel is sliced into 256 sub-lanes, and each symbol stretches to about thirteen millionths of a second: hundreds of times longer than the room's echoes. A copy arriving thirty or fifty billionths of a second late barely smudges the opening moment of a symbol that long. Real radios even pad each symbol's start, a small guard interval, which is nothing more than a polite pause to let the echoes die down before the symbol proper begins. But don't take the arithmetic's word for it. Below is the same room and the same stubborn echo you just fought with; this time the slider is the fix. Slice the channel yourself and watch what the echo can still reach.
short symbols: the echo lands on the first 89% of every one
The scheme has a mouthful of a name, orthogonal frequency-division multiplexing, OFDM for short, and having said it once we can call it what it really is: an orchestra. One singer racing through the lyrics trips over the hall's own echo. Hand the same lyrics to a choir, one voice per line, each voice holding one slow, steady note at its own pitch, and the hall can echo all it likes. The same syllables per second arrive, and nobody is drowned out by their own reflection.
This is not some exotic laboratory curiosity. It is what your gadgets actually speak, almost all of them, almost all the time. Wi-Fi is an orchestra. So are 4G and 5G, each phone handed its own bundle of subcarriers. Digital television spreads a picture across thousands of slow carriers, and DAB digital radio sings with about fifteen hundred. Whenever bits move fast through a world full of walls, you will find a choir, not a soloist.
When a singer goes hoarse#
The orchestra has one more virtue, and it may be the most graceful thing in this book. Remember chapter 4's dead spots: a bounced copy canceling the direct wave in one unlucky place. The same bouncing can cancel in one unlucky frequency, too, parking a dead spot on a few sub-lanes of the shelf while their neighbors stay perfectly clean. A single fast stream using the whole shelf would limp everywhere at once. The orchestra just reseats itself.
Your laptop and router are already measuring the channel constantly; that was last chapter's negotiation. The wired cousins of Wi-Fi, the DSL and cable modems piping the internet through old phone lines and coax, run that negotiation lane by lane: they load six dense bits onto every healthy subcarrier, drop to sturdy two-bit QPSK where the shelf gets rough, and let a hopeless lane rest entirely. It's exactly like giving a hoarse singer an easier part while the rest of the choir carries the tune. Wi-Fi keeps it simpler: it picks one modulation for the whole channel and leans on chapter 19's error correction, woven across all the subcarriers, to heal the few lanes a dead spot spoils. Either way the link doesn't break; it barely even slows. (Some interference is less polite than a dead spot, of course. It growls, it hops, it picks fights. Radios have an answer for that too, three chapters from now.)
One chip, a whole choir#
One honest confession before we close. Hundreds of perfectly spaced carriers may sound like hundreds of tiny transmitters humming shoulder to shoulder inside your router. There is one. A single chip takes the list of ingredients it wants (every subcarrier, each holding its chosen symbol) and runs chapter 16's recipe math backward, cooking up the single lumpy wave that whole stack adds up to. Fourier's idea in reverse (the method itself is unpacked in the un-adding machine, if you're curious), performed tens of thousands of times every second, and the entire choir pours out of one antenna as one wave.
So hold the picture. The room itself sets a speed limit on any one fast talker, because past a certain pace you trip over your own echo, and shouting louder only makes the echo louder. The sidestep is to stop racing: send hundreds of slow streams side by side on one shelf, each symbol so long that the echoes die inside it. That is the wave leaving your laptop right now.
One question is left begging, though. This whole part of the book has been an escalation: one bit per symbol, then six, then a choir singing symbols side by side. Every chapter found a way to go faster, and nothing ever seemed to push back. Does it end? Could a cleverer radio, someday, send anything at any speed? It turns out there is a wall, it was discovered before almost any of this existed, and it is written in arithmetic simple enough for a picture book. The speed limit is next.