Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. 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 for the problem of finding a code that has both exponentially decreasing error probabi ...Full description
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. 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 for the problem of finding a code that has both exponentially decreasing error probability with increasing block length and polynomial-time decoding complexity. Let C be a code with length N and rate R over an alphabet A with K=N*R symbols. Let I be another code with length n and rate r over an alphabet B with k=n*r symbols. The inner code I takes one of k possible inputs, encodes onto an n-tuple from B, transmits, and decodes into one of k possible outputs. We regard this as a (super) channel which can transmit one symbol from the alphabet A, also of size k. We use this channel N times to transmit each of the N symbols in a codeword of C. The concatenation of C (as outer code) with I (as inner code) is thus a code of length Nn over the alphabet B.