Pulse-code modulation

Pulse-code modulation (PCM) is a digital representation of an analog signal where the magnitude of the signal is sampled regularly at uniform intervals, then quantized to a series of symbols in a digital (usually binary) code. PCM is used in digital telephone systems and is also the standard form for digital audio in computers and various compact disc formats. It is also standard in digital video. Very frequently, PCM encoding facilitates digital transmission from one point to another (within a given system, or geographically) in serial form.

In the diagram to the right, a simple signal is quantized and sampled. For example, in the figure to the right of this paragraph, a sine wave (red curve) is sampled at regular intervals, shown as ticks on the x-axis. For each sample, one of the available values (ticks on the y-axis) is chosen by some algorithm (in this case, the floor function is used). This produces a fully discrete representation of the input signal (shaded area) that can be easily encoded as digital data for storage or manipulation. For the sine wave example at right, we can verify that the values at the sampling moments are 9, 11, 12, 13, 14, 14, 15, 15, 15, 14, etc. The integers are translated into a binary representation; the PCM data encoding would look like this in binary: 1001, 1011, 1100, 1101, 1110, 1110, 1111, 1111, 1111, 1110, etc.

It may be noted that in the picture that there are two sources of impairment:

rounding the analog signal to the nearest integer value, quantization error,
the frequency range of the analog signal is higher than half the sampling rate, aliasing error.

When reproducing the data as an analog signal, the discrete signal will be passed through analog filters or is interpolated using digital filters that suppress artifacts outside the expected frequency range of the output. In some systems, no explicit filtering is done at all; as it's impossible for any system to reproduce a signal with infinite bandwidth, inherent losses in the system compensate for the artifacts. Provided that the sampling frequency is sufficiently greater than that of the input signal, almost all of the induced noise can be effectively filtered out, resulting in an accurate (albeit phase shifted) representation of the original input.

Several Pulse Code Modulation streams may be multiplexed into a larger aggregate data stream. This technique is called time-division multiplexing, or TDM.

Digitization as part of the PCM process

In conventional PCM, the analog signal may be processed (e.g. by amplitude compression) before being digitized. Once the signal is digitized, the PCM signal is usually subjected to further processing (e.g. digital data compression).

Some forms of PCM combine signal processing with coding. Older versions of these systems applied the processing in the analog domain as part of the A/D process, newer implementations do so in the digital domain. These simple techniques have been largely rendered obsolete by modern transform-based signal compression techniques.

Differential (or Delta) pulse-code modulation (DPCM) encodes the PCM values as differences between the current and the previous value. For audio this type of encoding reduces the number of bits required per sample by about 25% compared to PCM.
Adaptive DPCM (ADPCM) is a variant of DPCM that varies the size of the quantization step, to allow further reduction of the required bandwidth for a given signal-to-noise ratio (SNR or S/N).

In telephony, a standard audio signal for a single phone call is encoded as 8000 analog samples per second, of 8 bits each, giving a 64 kbit/s digital signal known as DS0. The default encoding on a DS0 is either μ-law (mu-law) PCM (North America and Japan) or A-law PCM (Europe and most of the rest of the world). These are logarithmic compression systems where a 12 or 13 bit linear PCM sample number is mapped into an 8 bit value. This system is described by international standard G.711.

Where circuit costs are high and loss of voice quality is acceptable, it sometimes makes sense to compress the voice signal even further. An ADPCM algorithm is used to map a series of 8 bit PCM samples into a series of 4 bit ADPCM samples. In this way, the capacity of the line is doubled. The technique is detailed in the G.726 standard.

Later it was found that even further compression was possible and additional standards were published. Some of these international standards describe systems and ideas which are covered by privately owned patents and thus use of these standards requires payments to the patent holders.

Some ADPCM techniques are used in Voice over IP communications.

Encoding the bitstream as a signal

Pulse-code modulation can be either return-to-zero (RZ) or non-return-to-zero (NRZ). For a NRZ system to be synchronized using in-band information, there must not be long sequences of identical symbols, such as ones or zeroes. For binary PCM systems, the density of 1-symbols is called 'ones-density'.

Ones-density is often controlled using precoding techniques such as Run Length Limited encoding, where the PCM code is expanded into a slightly longer code with a guaranteed bound on ones-density before modulation into the channel. In other cases, extra 'framing' bits are added into the stream which guarantee at least occasional symbol transitions.

Another technique used to control ones-density is the use of a 'scrambler' polynomial on the raw data which will tend to turn the raw data stream into a stream that looks pseudo-random, but where the raw stream can be recovered exactly by reversing the effect of the polynomial. In this case, long runs of zeroes or ones are still possible on the output, but are considered unlikely enough to be within normal engineering tolerance.

In other cases, the long term DC value of the modulated signal is important, as building up a DC offset will tend to bias detector circuits out of their operating range. In this case special measures are taken to keep a count of the cumulative DC offset, and to modify the codes if necessary to make the DC offset always tend back to zero.

Many of these codes are bipolar codes, where the pulses can be positive, negative or absent. Typically, non-zero pulses alternate between being positive and negative. These rules may be violated to generate special symbols used for framing or other special purposes.

History of PCM

In retrospect, PCM, like many other great inventions, appears to be simple and obvious. In the history of electrical communications, the earliest reason for sampling a signal was to interlace samples from different telegraphy sources, and convey them over a single telegraph cable. Telegraph time-division multiplex (TDM) was conveyed as early as 1853, by the American inventor M.B. Farmer. The electrical engineer W.M. Miner, in 1903, used an electro-mechanical commutator for time-division multiplex of multiple telegraph signals, and also applied this technology to telephony. He obtained intelligible speech from channels sampled at a rate above 3500–4300 Hz: below this was unsatisfactory.

PCM was invented by the British engineer Alec Reeves in 1937 while working for the International Telephone and Telegraph in France. He had filed for a French patent in 1938, his U.S. patent was granted in 1943.

The first transmission of speech by digital techniques was the SIGSALY vocoder encryption equipment used for high-level Allied communications during World War II from 1943.

It was not until about the middle of 1943 that Bell Labs people who designed the sigsaly system, became aware of the use of PCM binary coding as already proposed by Alec Reeves.

Nomenclature

The word pulse in the term Pulse-Code Modulation is somewhat confusing, as there appear to be no "pulses" per se anywhere to be found. This perhaps is a natural consequence of this technique having evolved alongside two others, Pulse width modulation and Pulse position modulation, in which the information to be encoded is in fact represented by binary signal pulses of varying width or position, respectively. In this respect, PCM bears no resemblance to these other forms of signal encoding, except that the binary numbers of the PCM codes are represented as electrical pulses.

References

Ken C. Pohlmann, Principles of Digital Audio, 2nd ed. Carmel, Indiana.: Sams/Prentice-Hall Computer Publishing, 1985, ISBN 0-672-22634-0.

External links

Ralph Miller and Bob Badgley invented PCM independently in their work at Bell Labs on SIGSALY: US Patent Number 3,912,868: N-ary Pulse Code Modulation.

Radio modulation modes | Audio codecs | Computer file formats