ScholarLens Back to search
2015•Unpublished venueRequires access

Linear Block Codes

Didier Le Ruyet, Mylène Pischella

Open publisher page 0 citations

Abstract

The aim of the channel coding is to protect data delivered by the source coder against transmission errors. There are three families of codes: linear block codes, convolutional codes and concatenated codes. This chapter examines the main properties of linear block codes applied to error correction and error detection. First, some fundamental notions of finite fields are given, which is followed by the study of linear block codes, their structures, properties and their matrix representations. Next, the chapter discusses the hard and soft input decoding algorithms for binary linear block codes. After analyzing their theoretical performance, it focuses on the class of cyclic codes and their properties. Hamming codes, Golay codes and Reed-Muller codes are also explained in the chapter. Some applications, and exercises for the reader are given at the end.

About this research paper

What this paper is about

The aim of the channel coding is to protect data delivered by the source coder against transmission errors. There are three families of codes: linear block codes, convolutional codes and concatenated codes. This chapter examines the main properties of linear block codes applied to error correction and error detection. First, some fundamental notions of finite fields are given, which is followed by the study of linear block codes, their structures, properties and their matrix representations. Next, the chapter discusses the hard and soft input decoding algorithms for binary linear block codes. After analyzing their theoretical performance, it focuses on the class of cyclic codes and their properties. Hamming codes, Golay codes and Reed-Muller codes are also explained in the chapter. Some applications, and exercises for the reader are given at the end.

Why it matters

A significance statement is not available in the OpenAlex record.

Key contribution

A contribution statement is not available in the OpenAlex record.

Method / approach

Method details are not available in the OpenAlex metadata.

Main findings

Findings are not separately available in the OpenAlex metadata.

Limitations

Limitations are not available in the OpenAlex metadata.

Applications

Application details are not available in the OpenAlex metadata.

Available abstract

The aim of the channel coding is to protect data delivered by the source coder against transmission errors. There are three families of codes: linear block codes, convolutional codes and concatenated codes. This chapter examines the main properties of linear block codes applied to error correction and error detection. First, some fundamental notions of finite fields are given, which is followed by the study of linear block codes, their structures, properties and their matrix representations. Next, the chapter discusses the hard and soft input decoding algorithms for binary linear block codes. After analyzing their theoretical performance, it focuses on the class of cyclic codes and their properties. Hamming codes, Golay codes and Reed-Muller codes are also explained in the chapter. Some applications, and exercises for the reader are given at the end.

Key concepts: Block code, Linear code, Hamming code, Concatenated error correction code, Serial concatenated convolutional codes, Turbo code, Tornado code, Luby transform code

Related papers

Related paper 1Related paper 2Related paper 3
Back to paper searchBrowse research topicsOriginal source
Linear Block Codes — Research Paper | ScholarLens