The chapter introduces basic Channel Coding definitions and properties first limiting the treatment to binary linear block codes. They are defined by the Parity-Check and Generator matrices. These matrices are shown for the single parity check code, the repetition code, the Hamming code, Reed-Muller codes and the binary Golay code. Duality is defined and the Standard Array outlines decoding alternatives either toward the center of a decoding sphere or the coset leader, i.e., the error pattern. As coding bounds, the Singleton and the Hamming (Sphere-Packing) bounds are provided.

错误:搜索内容不能为空,请输入英文关键词
错误:关键词超出字数限制,请精简
高级检索

Basic Coding Definitions and Some Block Codes

  • Werner Henkel

摘要

The chapter introduces basic Channel Coding definitions and properties first limiting the treatment to binary linear block codes. They are defined by the Parity-Check and Generator matrices. These matrices are shown for the single parity check code, the repetition code, the Hamming code, Reed-Muller codes and the binary Golay code. Duality is defined and the Standard Array outlines decoding alternatives either toward the center of a decoding sphere or the coset leader, i.e., the error pattern. As coding bounds, the Singleton and the Hamming (Sphere-Packing) bounds are provided.