Fundamentals of Error-Correcting Codes,W.Cary Huffman and Vara Pless

In 1948 Claude Shannon published a landmark paper "A mathematical theory of communication" that signified the beginning of both information theory and coding theory. Given a communication channel which may corrupt information sent over it, Shannon identified a number called the capacity of the channel and proved that arbitrarily reliable communication is possible at any rate below the channel capacity. For example, when transmitting images of planets from deep space, it is impractical to retransmit the images. Hence if portions of the data giving the images are altered, due to noise arising in the transmission, the data may prove useless. Shannon's results guarantee that the data can be encoded before transmission so that the altered data can be decoded to the specified degree of accuracy. Examples of other communication channels include magnetic storage devices, compact discs, and any kind of electronic communication device such as cellular telephones (ISBN2: 0521782805).

The common feature of communication channels is that information is emanating from a source and is sent over the channel to a receiver at the other end. For instance in deep space communication, the message source is the satellite, the channel is outer space together with the hardware that sends and receives the data, and the receiver is the ground station on Earth. (Of course, messages travel from Earth to the satellite as well.) For the compact disc, the message is the voice, music, or data to be placed on the disc, the channel is the disc itself, and the receiver is the listener. The channel is "noisy" in the sense that what is received is not always the same as what was sent. Thus if binary data is being transmitted over the channel, when a 0 is sent, it is hopefully received as a 0 but sometimes will be received as a 1 (or as unrecognizable). Noise in deep space communications can be caused, for example, by thermal disturbance. Noise in a compact disc can be caused by fingerprints or scratches on the disc. The fundamental problem in coding theory is to determine what message was sent on the basis of what is received.