6 - Serial concatenation and RA codes

Summary

The idea of concatenating two or more error correction codes in series in order to improve the overall decoding performance of a system was introduced by Forney in 1966. Applying random-like interleaving and iterative decoding to these codes gives a whole new class of turbo-like codes that straddle the gap between parallel concatenated turbo codes and LDPC codes.

Concatenating two convolutional codes in series gives serially concatenated convolutional codes (SC turbo codes). We arrive at turbo block codes by concatenating two block codes and at repeat–accumulate codes by concatenating a repetition code and a convolutional (accumulator) code.

This chapter will convey basic information about the encoding, decoding and design of serially concatenated (SC) turbo codes. Most of what we need for SC turbo codes has already been presented in Chapter 4. The turbo encoder uses two convolutional encoders, from Section 4.2, while the turbo decoder uses two copies of the log BCJR decoder from Section 4.3. The section on design principles will refer to information presented in Chapter 5 and the discussion of repeat–accumulate codes will use concepts presented in Chapter 2. A deeper understanding of SC turbo codes and their decoding process is explored in Chapters 7 and 8.

Serial concatenation

The first serial concatenation schemes concatenated a high-rate block code with a short convolutional code. The first code, called the outer code, encoded the source message and passed the resulting codeword to the second code, called the inner code, which re-encoded it to obtain the final codeword to be transmitted.