What is the difference between baud rate and bit rate?

Question

I am really having hard time understanding the difference. Some say they are same, while others say there is a slight difference. What's the difference, exactly? I would like it if you explained with some analogy.

Answer 1

Bits per second is straightforward. It is exactly what it sounds like. If I have 1000 bits and am sending them at 1000 bps, it will take exactly one second to transmit them.

Baud is symbols per second. If these symbols — the indivisible elements of your data encoding — are not bits, the baud rate will be lower than the bit rate by the factor of bits per symbol. That is, if there are 4 bits per symbol, the baud rate will be ¼ that of the bit rate.

This confusion arose because the early analog telephone modems weren't very complicated, so bps was equal to baud. That is, each symbol encoded one bit. Later, to make modems faster, communications engineers invented increasingly clever ways to send more bits per symbol.¹

Analogy

System 1, bits: Imagine a communication system with a telescope on the near side of a valley and a guy on the far side holding up one hand or the other. Call his left hand "0" and his right hand "1," and you have a system for communicating one binary digit — one bit — at a time.

System 2, baud: Now imagine that the guy on the far side of the valley is holding up playing cards instead of his bare hands. He is using a subset of the cards, ace through 8 in each suit, for a total of 32 cards. Each card — each symbol — encodes 5 bits: 00000 through 11111 in binary.²

Analysis

The System 2 guy can convey 5 bits of information per card in the same time it takes the System 1 guy to convey one bit by revealing one of his bare hands.

You see how the analogy seems to break down: finding a particular card in a deck and showing it takes longer than simply deciding to show your left or right hand. But, that just provides an opportunity to extend the analogy profitably.

A communications system with many bits per symbol faces a similar difficulty, because the encoding schemes required to send multiple bits per symbol are much more complicated than those that send only one bit at a time. To extend the analogy, then, the guy showing playing cards could have several people behind him sharing the work of finding the next card in the deck, handing him cards as fast as he can show them. The helpers are analogous to the more powerful processors required to produce the many-bits-per-baud encoding schemes.

That is to say, by using more processing power, System 2 can send data 5 times faster than the more primitive System 1.

Historical Vignette

What shall we do with our 5-bit code? It seems natural to an English speaker to use 26 of the 32 available code points for the English alphabet. We can use the remaining 6 code points for a space character and a small set of control codes and symbols.

Or, we could just use Baudot code, a 5-bit code invented by Émile Baudot, after whom the unit "baud" was coined.³

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Footnotes and Digressions:

1. For example, the V.34 standard defined a 3,429 baud mode at 8.4 bits per symbol to achieve 28.8 kbit/sec throughput.

   That standard only talks about the POTS side of the modem. The RS-232 side remains a 1 bit per symbol system, so you could also correctly call it a 28.8k baud modem. Confusing, but technically correct.

2. I've purposely kept things simple here.

   One thing you might think about is whether the absence of a playing card conveys information. If it does, that implies the existence of some clock or latch signal, so that you can tell the information-carrying absence of a card from the gap between the display of two cards.

   Also, what do you do with the cards left over in a poker deck, 9 through King, and the Jokers? One idea would be to use them as special flags to carry metadata. For example, you'll need a way to indicate a short trailing block. If you need to send 128 bits of information, you're going to need to show 26 cards. The first 25 cards convey 5×25=125 bits, with the 26th card conveying the trailing 3 bits. You need some way to signal that the last two bits in the symbol should be disregarded.

3. This is why the early analog telephone modems were specified in terms of baud instead of bps: communications engineers had been using that terminology since the telegraph days. They weren't trying to confuse bps and baud; it was simply a fact, in their minds, that these modems were transmitting one bit per symbol.