Range coding (or range encoding) is an entropy coding method defined by G. Nigel N. Martin in a 1979 paper, which effectively rediscovered the FIFO arithmetic code first introduced by Richard Clark Pasco in 1976. Given a stream of symbols and their probabilities, a range coder produces a space-efficient stream of bits to represent these symbols and, given the stream and the probabilities, a range decoder reverses the process. Range coding is very similar to arithmetic coding, except that coding is done with digits in any base, instead of with bits, and so it is faster when using larger bases (e.g. a byte) at small cost in compression efficiency. After the expiration of the first (1978) arithmetic coding patent, range coding appeared to clearly be free of patent encumbrances. This particularly drove interest in the technique in the open source community. Since that time, patents on various well-known arithmetic coding techniques have also expired. How range coding works Range coding conceptually encodes all the symbols of the message into one number, unlike Huffman coding which assigns each symbol a bit-pattern and concatenates all the bit-patterns together. Thus range coding can achieve greater compression ratios than the one-bit-per-symbol lower bound on Huffman coding and it does not suffer the inefficiencies that Huffman does when dealing with probabilities that are not an exact power of two. The central concept behind range coding is this: given a large-enough range of integers, and a probability estimation for the symbols, the initial range can easily be divided into sub-ranges whose sizes are proportional to the probability of the symbol they represent. Each symbol of the message can then be encoded in turn, by reducing the current range down to just that sub-range which corresponds to the next symbol to be encoded. The decoder must have the same probability estimation the encoder used, which can either be sent in advance, derived from already transferred data or be part of the compressor and decompressor. When all symbols have been encoded, merely identifying the sub-range is enough to communicate the entire message (presuming of course that the decoder is somehow notified when it has extracted the entire message). A single integer is actually sufficient to identify the sub-range, and it may not even be necessary to transmit the entire integer; if there is a sequence of digits such that every integer beginning with that prefix falls within the