A method of transmitting a digital approximation to an analogue signal, pulse code modulation (PCM) is used in all modern audio and telecommunications equipment, from the MiniDisc to the cell phone.

PCM was invented in 1937 by Alec Reeves as a means of high fidelity communication, and it was used by the Allied military as a means of transmitting coded messages during World War II. Reeves' digital invention depended on expensive racks of valves, and his 1938 patent expired before the low-cost transistor made it economically viable on a wider scale. For his invention, Reeves was awarded the Ballantine Medal of the Franklin Institute in 1965, and the City of Columbus Gold Medal in 1966.

PCM is a very simple concept to understand. An analogue signal is sampled at a given sampling frequency, fs; this gives a sampling period of Ts = 1/fs. Every Ts seconds, the analogue signal is quantized to one of N levels. Each level is assigned an integer value, and a code representing this value is transmitted over the channel. The code is transmitted as a series of pulses: most commonly, the code will be binary, and there will be one pulse for each bit value.

The bit rate of a PCM signal is given by fs * log2(N). The fidelity of a signal can be increased by increasing either the sampling frequency (giving a wider range of frequencies) or the number of quantization levels (giving a more accurate sample). For example, a land line telephone signal has a sampling frequency of 8KHz, and 256 quantization levels, giving a bit rate of 8000 * log2(256) = 8000 * 8 = 64Kbit/s. A compact disc has a sampling frequency of 44.1KHz, and 65536 quantization levels, giving a bit rate of 705Kbit/s per channel; the stereo bit rate is 1410Kbit/s.

A simple example of a possible binary code and its associated pulses is:

```Value   Code   Pulse Code
-------------------------
0      00    :    :    :
:____:____:

1      01    :    :_   :
:____| |__:

2      10    :_   :    :
| |__:____:

3      11    :_   :_   :
| |__| |__:
```

Each division made by colons is a transmitted pulse width: the pulse for a 0 bit value is represented by a flat pulse; the pulse for a 1 bit value has the voltage asserted for half the pulse width. The reason for this width is to stop a slightly over-long voltage assertion from being interpreted as two consecutive one-values.

The advantages of PCM are extensive. One of the most important properties of the method is that a PCM signal may be entirely reconstructed: in long distance communications, repeater stations can decode and re-encode the signal with no loss of information. This means that the effects of line noise do not accumulate, and an entirely clean signal can be sent at each hop.

Another crucial ability given by PCM is the potential to use more efficient coding schemes. For example, source coding using the Shannon-Fano algorithm allows far higher efficiency than a simple binary code representing the same information. With no loss of content, data may be sent using far fewer symbols, and thus at a lower cost to the user.

Variations of PCM include Differential Pulse Code Modulation and Adaptive Differential Pulse Code Modulation. Both of these schemes reduce the transmission of data by differentially encoding the data stream, sending only deltas against the previous value.

Sources:

Alec Harley Reeves: TelecomWriting.com
Introduction to Communication Systems, Ferrel G. Stremler, Addison-Wesley
Data Communications and Networks: An Engineering Approach, Irvine & Harle, Wiley