Background
In communication systems, Source Coding is the process of encoding the output of an information source into a format that can be transmitted digitally to a receiver as a series of code words such that the average length of the code words is as small as possible. This reduction in redundancy is also known as data compression. The smallest theoretically achievable average code word length for lossless compression is equal to the entropy of the source. Further compression is possible only if it is lossy .
Data compression is made possible and also is made necessary by digital representation of signals. For example, an analog television system with a video bandwidth of 4 MHz is capable of transmitting 8 million analog samples of a picture per second. These samples hypothetically may have any independent analog values representing picture brightness at discrete points or pixels. The amplitude precision of these analog samples is limited only by the signal to noise ratio in the channel.
In a digital representation of the signal, however, each (monochrome) pixel may be represented (for example) by 8 bits, thus expanding the number of samples to be transmitted by 8 times! The first reduction in this required bandwidth is often use of multilevel signals that can transmit more than one bit per transmitted sample (or symbol). Thus, two-level symbols transmit 1 bit per symbol, four level symbols transmit 2 bits per symbol, and 256-level symbols transmit 8 bits per symbol. Using 256-level transmission, however, offers no advantage over analog transmission, as noise will easily cause errors in discriminating between levels unless very high signal power can be maintained. Similar arguments apply to the recording of video on tape or other media.
In the case of broadcast transmission, 4-level symbols appear to be a practical limit; for cable TV, 16 levels is about the practical limit.
If we take the ratio of the bits per pixel to the number of bits per symbol, we can see that a digital monochrome system will require a compression ratio of about 4:1 (8 bits per pixel / 2 bits per symbol) to fit in the same bandwidth as an analog system. What is lost in the digital system is the capability to transmit the values directly; but what is gained is the robustness of the digital transmission. Of course, we wish to transmit color information as well, which may increase the input information by 50% to 200% additional (depending on possible subsampling of the color information).
Once compression technology is applied, it may be used to obtain higher compression ratios in order to transmit a greater source bandwidth, such as a high definition program or multiple standard definition programs, in the same channel size as a single standard definition analog program.