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Maximum a Posteriori Decoding of Turbo Codes

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The optimum decoding procedure for turbo codes is the maximum a posteriori (MAP) algorithm. The MAP decoding algorithm has some similarities to the Viterbi decoding algorithm; the major difference is that the Viterbi algorithm is not equipped to output soft-decision bits that turbo decoding requires. This article gives a detailed mathematical development of the MAP algorithm, illustrating with a step-by-step numerical example how to use the MAP algorithm.
This article is excerpted from Digital Communications: Fundamentals and Applications, Second Edition (Prentice-Hall, 2001, ISBN 0-13-084788-7).
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The process of turbo-code decoding starts with the formation of a posteriori probabilities (APPs) for each data bit, which is followed by choosing the data-bit value that corresponds to the maximum a posteriori (MAP) probability for that data bit. Upon reception of a corrupted code-bit sequence, the process of decision-making with APPs allows the MAP algorithm to determine the most likely information bit to have been transmitted at each bit time. The metrics needed for the implementation of a MAP decoder are presented here, along with an example to illustrate how these metrics are used.

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Editor's Note: This article is offered in PDF in order to provide consistency and clarity to the in-text equations.

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