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Viterbi Detection

Abstract – Turbo codes allow engineers to implement systems that use a low energy quantity for the emitter and still can reach the absolute maximum capacity of the channel (as defined by Shannon). This paper presents a practical software implementation of a turbo encoder-decoder and analyzes its performances against other encoding and recording solutions, such as PRML [1] channels and MTR-RLL [5] codes. Simulations confirmed the significant performance gains introduced by turbo codes and proved that a future hardware implementation of the turbo encoder and decoder components would be useful.
1. INTRODUCTION

Within a coding scheme it is important to find a compromise between the coding gain and the encoder complexity. Usually this is done through concatenation. A concatenated code is a code that uses two levels of encoding, an interior one and an exterior one, linked by an interleaver, as seen in figure 1.

Figure 1. Block diagram for a typical turbo encoder-decoder. [8]

The main advantage of a concatenated code is obtaining a minimum bit error rate (BER) with a smaller general decoding complexity as compared to a standard code

with the same performance. The small complexity is obtained by decoding each code component separately.
A turbo code extends the properties of concatenated codes through the fact that it concatenates two convolutional codes in parallel. The convolutional codes are systematic. The exterior code does not transmit the input bits, which reduces the code rate. The interleaver has a very important role in the efficient functionality of the encoder. It prevents the decoder from receiving block errors, which are difficult to correct, by spreading these errors inside the input sequence, increasing the distance between them and decorelating the input symbols. The interleaver size is an important parameter, as the coding gain is directly proportional to it.
Two decoders, connected through the same interleaver, perform the decoding...