Chapter 16Low‐Density Parity‐Check Codes: Designs and Variations

16.1 Introduction

This chapter builds on the LDPC foundations of the previous chapter to present ideas related to the analysis of LDPC codes and several design methodologies.

The chapter begins (Section 16.2) with a description of repeat‐ accumulate (RA) and irregular repeat‐accumulate (IRA) codes, codes which have low encode complexity and good performance.

LDPC convolutional codes (LDPCCC) are presented in Section 16.3. These are LDPC codes which have a convolutional structure which provides for low encode complexity.

Then several design methodologies are presented, starting with a generalization of cyclic codes known as quasi‐cyclic (QC) codes (Section 16.4). Many of the LDPC designs are based on QC codes. These designs provide connections between some of the coding and field theory of earlier chapters to LDPC codes.

The chapter continues (Section 16.7) with a description of ensembles of LDPC codes. The presentation here is merely descriptive, but these ensembles are used sometimes in design algorithms. Code design using progressive edge growth (PEG) is then described (Section 16.8) and protograph and multi‐edge‐ type LDPC codes (Section 16.9).

Trapping sets have been explored as causing error floors in LDPC codes. Trapping sets are examined briefly in Section 16.10.

Attention then turns to importance sampling in Section 16.11. This is a topic not directly related to LDPC codes, but seemed appropriate to include ...

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