Error Correction Coding, 2nd Edition

Chapter 11Soft‐Decision Decoding Algorithms

11.1 Introduction and General Notation

Most of the decoding methods described to this point in the book have been based on discrete field values, usually bits obtained by quantizing the output of the matched filter. However, the actual value of the matched filter output might be used, instead of just its quantization, to determine the reliability of the bit decision. For example, in BPSK modulation if the matched filter output is very near to zero, then any bit decision made based on only that output would have low reliability. A decoding algorithm which takes into account reliability information or uses probabilistic or likelihood values rather than quantized data is called a soft‐decision decoding algorithm. Decoding which uses only the (quantized) received bit values and not their reliabilities is referred to as hard‐decision decoding. As a general rule of thumb, soft‐decision decoding can provide as much as 3 dB of gain over hard‐decision decoding. In this short chapter, we introduce some of the most commonly used historical methods for soft‐decision decoding, particularly for binary codes transmitted using BPSK modulation over the AWGN channel. Some modern soft‐decision decoding techniques are discussed in the context of turbo codes (Chapter 14) and LDPC codes (Chapter 15) and polar codes (Chapter 17).

Some clarification in the terminology is needed. The algorithms discussed in the chapter actually provide hard output decisions. ...