Chapter 2

Decoding

Moshe Ran,1 Carlos De Segovia,2 Omer Ran3

1Holon Institute of Technology, Israel

2Orange Labs, France

3MostlyTek Ltd, Israel

This chapter provides an overview of efficient soft-decision decoding techniques. We survey maximum-likelihood soft-decision decoding (ML-SDD) algorithms, which are relatively simple to apply for short-length codes. A novel algorithm based on a soft-syndrome decoder is presented, and the interesting topic of SDD algorithms for Reed–Solomon codes is introduced in. We focus on maximum a posteriori probability (MAP) decoding, which underlies the iterative decoding algorithms for random-like long codes including turbo codes and LDPC codes. Both approaches are considered optimal. However, in MAP decoding the optimality condition minimizes the information bit or symbol error rate, whereas maximum-likelihood decoding (MLD) minimizes the codeword error rate.

Techniques and results relevant for the decoding of short packets are highly valued in the context of error control coding of next-generation wireless systems. We use the imperfectness of a given code [DDP98] as a figure of merit for code performance over the AWGN channel. It is defined as the difference between the code's required Eb/N0 to attain a given word error probability (Pw), and the minimum possible Eb/N0 required to attain the same Pw, as implied by the sphere-packing bound (SPB) of Shannon [SH59] for codes with the same block size k and code rate r. We note that the original SPB ...

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