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2.5: Serial Concatenation

By U. Vilaipornsawai
From Turbo Coding for Satellite and Wireless Communications

2.5 Serial Concatenation

A serial concatenated code was first conceived by Forney [46], see Figure 2.16. It was shown that the probability of error for serial concatenated codes decreases exponentially as the frame size increases at rates less than capacity while decoding complexity increases only algebraically.


Figure 2.16: Serial Concatenation Codes

The outer encoder produces outer code symbols (or sequences of symbols) that enter the inner encoder as information symbols (sequences). The inner encoder, in turn, produces inner code symbols that are transmitted using some memoryless modulation. Forney showed that the optimal concatenated receiver consists of an inner detector producing a posteriori probabilities (APP) of the inner information symbols, which are then used in the outer detector.

The best known example is a Reed-Solomon (RS) outer code concatenated with a convolutional inner code separated by a symbol interleaver. A SCCC is the result of combining the features of serial concatenated codes with those of turbo codes. Unlike the symbol interleaver between RS and the convolutional code, a bit interleaver is used in SCCCs to introduce randomness.

2.5.1 Structure of SCCC

Using the same components as the turbo codes, such as constituent encoders, the interleaver, the puncturer, and the soft-input soft-output MAP decoders, another type of concatenated codes, serial concatenated convolutional codes (SCCCs), were proposed [59]. The good performance of SCCCs has led to a lot of investigations and applications in the coding field.

The basic structure of a SCCC encoder is shown in Figure 2.17, where u

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