Concatenated codes

In coding theory, concatenated codes form a class of error-correcting codes that are derived by combining an inner code and an outer code. They were conceived in 1966 by Dave Forney as a solution to the problem of finding a code that has both exponentially decreasing error probability with increasing block length and polynomial-time decoding complexity. Concatenated codes became widely used in space communications in the 1970s.

The field of channel coding is concerned with sending a stream of data at the highest possible rate over a given communications channel, and then decoding the original data reliably at the receiver, using encoding and decoding algorithms that are feasible to implement in a given technology.

Shannon's channel coding theorem shows that over many common channels there exist channel coding schemes that are able to transmit data reliably at all rates ${\displaystyle R}$ less than a certain threshold ${\displaystyle C}$, called the channel capacity of the given channel. In fact, the probability of decoding error can be made to decrease exponentially as the block length ${\displaystyle N}$ of the coding scheme goes to infinity. However, the complexity of a naive optimum decoding scheme that simply computes the likelihood of every possible transmitted codeword increases exponentially with ${\displaystyle N}$, so such an optimum decoder rapidly becomes infeasible.

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