A binary code assigns a finite binary word

c_{k}

to each source symbol

x_{k}

. In the ordinary unframed convention these codewords are nonempty. It is uniquely decodable when concatenation gives an injective map from finite symbol strings to bit strings:

c_{i_{1}} \dots c_{i_{r}} = c_{j_{1}} \dots c_{j_{s}} ⟹ r = s and i_{t} = j_{t} for all t .

(1)

The decoder can recover the entire symbol sequence without being told where codewords end. This is stronger than merely assigning distinct words to individual symbols.

An instantaneous code can decode each symbol as soon as its final bit arrives, without waiting for later bits. Equivalently it is prefix-free: no codeword is a proper prefix of another, and different symbols receive different codewords.

For nonempty codewords, decoding greedily from the start of the bit string identifies the first codeword unambiguously; repeating identifies the whole sequence. Thus an instantaneous code is uniquely decodable under the ordinary nonempty-word convention.