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Text File | 1994-11-23 | 3KB | 74 lines

Compact Disc Data Transfer Rates

Andrew Davidson
Philips Interactive Media of America


This note is an attempt to provide a derivation of the standard CD-ROM data
rate of 150 kb per second. In this note, "kb" means kilobyte, "mb" means
megabyte, and "Mb" means megabit. A byte is 8 bits. A kilobyte is 1024 bytes
(not 1000 bytes!). I claim that a megabyte is only 1000 kilobytes, not 1024,
but there is some debate about that. I don't have a definitive answer.

It all starts with CD-DA (digital audio used for music CDs). CD-DA is sampled
at 44.1 khz. This means that there are 44,100 samples (or digital values) of
audio per second. In PCM audio, which is the standard for CD-DA, samples are
16 bits per channel. So for stereo, that means 32 bits per sample or 4 bytes.
Multiplying by 44,100 gives 176,400 bytes per second, or ~172 kb, remembering
that a kilobyte is 1024 bytes, not 1000 bytes:

  44100 * 4 / 1024 = 172.26 kb

So if CDs can transfer at 172 kb per second, where does the 150 kb figure come
from? We seem to have lost 22 kb per second.

Digital audio data is a continuous stream of bits on disc - there are no
sectors or files, only a table of contents tucked away on the disc that tells
your CD player where each track begins in that stream. For CD-ROM, we
obviously need some method of putting data into discrete chunks, or sectors.
The Yellow Book (the spec for CD-ROM) defines this method.

Sectors on CD-ROM discs are 2352 bytes each and are transferred at the rate of
75 per second. So:

  2352 * 75 = 176,400

and that number should be familiar from above: ~172 kb.

CD-DA data is very tolerant of errors in the data stream. Even if you "lose"
4 bytes during a transfer, that is only 1/44,100-th of a second of audio and
the human ear (brain, actually) hardly notices the loss. But if we lose 4
bytes of computer data randomly while using our CD-ROM disc, someone is likely
to get upset. So, each CD-ROM sector reserves 304 bytes of those 2352 for
error detection and error correction codes. These codes guarantee that
transfer errors can always be corrected, protecting the integrity of the data.
(Of course, it can't necessarily recover from peanut butter or scratches on
the disc.)  So now we have fewer bytes in each sector actually available for
user data:

  2352 - 304 = 2048 bytes per sector, and
  2048 * 75 sectors per second = 153,600 bytes per second
  153600 / 1024 = 150.0 kb per second

Therewith, the mythical 150 kb per second.

Newer double speed CD-ROM drives have to transfer at this rate to support
CD-DA, but can also go faster (150 sectors per second) for computer data to
achieve the 300 kb per second rate.

One also hears transfer rates quoted in terms of megabits per second (Mb).
Remembering that a byte is 8 bits, we can recast the 150 kb figure in terms
of Mb:

  150 * 8 * 1024 = 1,228,800 bits per second
  1228800 / 1024 / 1000 = 1.2 megabits per second

So 150 kb per second equals 1.2 Mb per second. You will often hear data
transfer rates for compressed digital video (like MPEG) referred to in Mb
per second. 1.2Mb per second is the nominal rate for optical disc-based
transmission of MPEG compressed video. In this case, we can sacrifice the
error correction data (since errors in real-time audio and video are also
less critical) and use the remaining bandwidth for MPEG compressed audio.
The total is then back to approximately 1.5 megabits per second, which
is compatible with CD-DA transfer rates.