Graph-Based Codes



The 1990s brought about classes of codes that are capable of performance near Shannon’s capacity limits for the most common channel models. These code classes include convolutional turbo codes, block turbo codes (BTCs), and low-density parity-check (LDPC) codes [1–6]. Each of these codes can be conveniently modeled by graphs. Such graphical models for codes lead to simplified decoder descriptions which in turn lead to an improved understanding of the performance characteristics of the decoders. A graphical description of a decoder has been well known since around 1970: the Viterbi decoder for decoding convolutional codes is generally described by a graph called a trellis. This chapter gives detailed introductions to parallel and serial convolutional turbo codes, BTCs, and LDPC codes. In discussing the decoding algorithms for each of these code classes, we chose the binary-input additive white Gaussian noise (AWGN) channel model to make our discussions more concrete. This channel model is appropriate for coherent optical communications, but is also often used as an approximation for photodetection receivers. Extensions to other channels require only modified decoder inputs.


LDPC Code Turbo Code Convolutional Code Extrinsic Information Tanner Graph 
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© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Department of Electrical & Computer EngineeringUniversity of ArizonaTucsonUSA

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