CD: Jitter, Errors & Magic Page 2
This encoding system elegantly solves a variety of data-retrieval functions. In EFM encoding, pit and land do not represent binary data directly. Instead, transitions from pit-to-land or land-to-pit represent binary one, while all other surfaces (land or pit bottom) represent binary zero. EFM encoding takes symbols of 8 bits and converts them into unique 14-bit words, creating a pattern in which binary ones are separated by a minimum of two zeros and a maximum of 10 zeros. The bit stream is thus given a specific pattern of ones and zeros that result in nine discrete pit or land lengths on the disc. The shortest pit or land length encodes three bits, while the longest encodes 11 bits. The blocks of 14 bits are linked by three "merging bits," resulting in an encoding ratio of 17:8. At first glance, it may seem odd that EFM encoding, in more than doubling the number of bits to be stored, can actually increase data density. But just this occurs: Storage density is increased by 25% over unmodulated encoding.
EFM has other inherent advantages. By inserting zeros between successive ones, the bandwidth of the signal reflected from the disc is decreased. The data rate from a CD is 4.3218 million bits per second (footnote 2), but the EFM signal has a bandwidth of only 720kHz. In addition, the EFM signal serves as a clock that, among other functions, controls the player's rotational servo.
The signal reflected from the disc is comprised of nine discrete frequencies, corresponding to the nine discrete pit or land lengths (footnote 3). The highest-frequency component, called "I3," is produced by the shortest pit or land length and has a frequency of 720kHz. This represents binary data 100. The lowest-frequency component, called "I11," is produced by the longest pit or land length and has a frequency of 193kHz. This represents binary data 10000000000. The signal reflected from the disc, produced by EFM encoding, is often called the HF (high frequency) signal. The varying periods of the sinewaves correspond to the periods of time required to read the various pit lengths.
At first impression, the HF signal appears to be analog, not one that carries digital data. However, the zero crossings of the waveforms contain the digital information encoded on the disc. Fig.2 shows the relationship between binary data, pit structure, and the recovered HF signal.
Fig.2 Relationship between binary data, pit structure, and the HF signal. (Reproduced from Principles of Digital Audio, Second Edition (1989), by Kenneth C. Pohlmann, with the permission of the publisher, Howard W. Sams & Company.)
HF signal quality is a direct function of pit shape, which in turn is affected by many factors during the CD manufacturing process. There is a direct correlation between error rates and pit shape. Poorly shaped pits result in a low-amplitude HF signal with poorly defined lines. Figs.3 and 4 show an excellent HF signal and a poor HF signal respectively.
Fig.3 A clean HF signal results from well-spaced pits.
Fig.4 A poor-quality HF signal.
CD data errors: Any digital storage medium is prone to data errors, and the CD is no exception. An error occurs when a binary one is mistakenly read as a binary zero (or vice versa), or when the data flow is momentarily interrupted. The latter, more common in CDs, is caused by manufacturing defects, surface scratches, and dirt or other foreign particles on the disc. Fortunately, the CD format incorporates extremely powerful error detection and correction codes that can completely correct a burst error of up to 4000 successive bits. The reconstructed data are identical to what was missing. This is called error correction. If the data loss exceeds the player's ability to correctly replace missing data, the player makes a best-guess estimate of the missing data and inserts this approximation into the data stream. This is called error concealment, or interpolation.
It is important to make the distinction between correction and concealment: correction is perfect and inaudible, while concealment has the potential for a momentary sonic degradation where the interpolation occurs.
A good general indication of disc quality (and the claimed error-reduction effects of some CD tweaks) is the Block Error Rate, or BLER. BLER is the number of blocks per second that contain errant data, before error correction. The raw data stream from a CD (called "channel bits") contains 7350 blocks per second, with a maximum allowable BLER (as specified by Philips) of 220. A disc with a BLER of 100 thus has 100 blocks out of 7350 with errant or missing data. In these experiments, Block Error Rate is the primary indicator of a particular tweak's effect on error-rate performance.
In addition to measuring the effects of CD tweaks on BLER, I explored their potential to reduce interpolations. To do this, I used the Pierre Verany test CD that has intentional dropouts in the spiral track. The disc has a sequence of tracks with increasingly long periods of missing data.
First, I found the track that was just above the threshold of producing an uncorrectable error (called an "E23 error") as analyzed by the Design Science CD Analyzer (see Sidebar). The track was played repeatedly to assure consistency, thus avoiding the ascription to chance of any subsequent change. Then, the same track was played and analyzed, this time after the addition of a CD treatment or device. This twofold approach—measuring a tweak's effect on both BLER and interpolations—would seem to cover the gamut of error-reduction potential.
There are two general misconceptions about CD errors and sound quality: 1) errors are the primary source of sonic degradation; and 2) if there are no uncorrectable errors, there can be no difference in sound.
The first conclusion is largely due to the marketing programs of CD-accessory manufacturers who claim their products reduce error rates. Many of the devices tested claim to improve sound quality by reducing the amount of error concealment performed by the CD player. In fact, interpolations (error concealment) rarely occur. In the unlikely event that concealment is performed, it will be momentary and thus have no effect on the overall sound. At worst, a transient tick or glitch would be audible.
To better understand the nature of data errors, a look at CD Read-Only Memory (CD-ROM) is useful. A CD-ROM is manufactured just like an audio CD, but contains computer data (text, graphics, application software, etc.) instead of music. The data retrieved from a CD-ROM must be absolutely accurate to the bit level, after error correction. If even a single wrong bit gets past the error correction, the entire program could crash. The errant bit may be within instructions for the host computer's microprocessor, causing the whole application to come to an instant halt, making the disc useless.
To prevent this, a quality-control procedure is routinely used at the mastering and pressing facility to assure 100% error-free performance. Samples of the finished CD-ROM are compared, bit for bit, to the original source data. For high-reliability applications, each replicated disc undergoes this process. This rigorous testing reveals much about the error-correction ability of the CD's Cross Interleaved Reed-Solomon encoding (CIRC). Throughout dozens of hours of this verification procedure, I cannot remember even a single instance of one wrong bit getting through.
It could be argued that CD-ROM has additional error-correction ability not found on CD audio discs. This is true, but the additional layer of error correction is almost never invoked. Furthermore, in all the hours of error-rate measuring for this project, I never encountered an E23 error, the first and most sensitive indication of an interpolation (except on the Pierre Verany disc, which has intentional errors). In fact, I saw only one E22 error, the last stage of correction before concealment. In retesting the disc, the E22 error disappeared, indicating it was probably due to a piece of dirt on the disc. Finally, the unlikely occurrence of an uncorrectable error is exemplified by the warning system in the Design Science CD Analyzer. The system beeps and changes the computer's display color to red to alert the operator if even an E22 error (fully corrected) is detected.
Footnote 2: Of this 4.3218 million bits per second, only 1.4 million bits are the basic audio data, the rest being redundant data, subcode data, and the result of the EFM transcoding.—Robert Harley
Footnote 3: Note that the varying frequencies refer to the intensity modulation of the reflected beam, not the frequency of the laser beam, which has a constant wavelength of 790 nanometers.—Robert Harley