Convolutional Codes and Turbo-Codes

Sergei Semenov1, and Andrey Trofimov2

1Nokia Corporation, Finland

2St. Petersburg State University of Aerospace Instrumentation, Russia

4.1 Convolutional Codes Representation and Encoding

The general structure of the convolutional encoder is represented in Figure 4.1. Every time moment the block of K symbols is fed to the input of the encoder. The encoder has the memory, which keeps the values of not more than ν – 1 previous input blocks (k · (ν – 1) symbols). The encoder forms n output symbols at a time. The block of n output symbols depends on k · ν input symbols and each output symbol is the linear combination of information symbols. The number k is called the number of information symbols, the number n is called the number of encoded symbols and the number ν is known as the constraint length of the code. The value is called the code rate. The corresponding convolutional code usually is denoted as (n, k, ν) code. Note that in some literature the used notation is (n, k, ν – 1).

Figure 4.1 A general convolutional encoder

The encoder works as follows: The input data block of k symbols is fed to k shift registers (each symbol to its own register) with the help of demultiplexer. Each shift register consists of no more than ν – 1 delay elements. ...

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