Communication systems in which messages are encoded by means of an inner code before being passed through a channel and then being decoded according to the inner code; this entire inner encoder-channel-decoder system is itself regarded as a channel (it is hoped less noisy than the original channel), and therefore has a further encoder and decoder placed before and after it; these implement an outer code. Alternatively, such a system may be considered as a channel with a compound encoder before it and a compound decoder after it, the compound encoder and decoder implementing a factorable code.
To a good approximation, the inner code should be designed to correct any channel errors arising in the original channel, while the outer code should be designed to cope with decoder errors occurring in the inner decoder. Since these decoder errors tend to occur in bursts, the outer code is usually a burst-error-correcting code: the Reed–Solomon codes are often used for this purie. The inner code is often a convolutional code.