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Algebraic Coding for Iterative Decoding

Algebraic Coding for Iterative Decoding

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Description
Since the publication of Shannon's 1948 paper ”A Mathematical Theory of Communication” the quest has been on to find practical channel coding schemes that live up to the promises given by Shannon. Traditionally, coding theory focused on finding codes with large minimum distance and then to find an efficient decoding algorithm for such a code. In the realm of iterative decoding the picture is reversed: given an iterative decoding algorithm, one has to look out for codes that are suitable for such an algorithm. To understand iterative decoding algorithms, it is advantageous to have a basic knowledge of factor graphs and the summary-product algorithm. Therefore, in a first step we show how the detection problems in a data transmission system can be modeled very naturally by factor graphs and solved with the help of the most popular instances of the generic summary-product algorithm, namely the sum-product and the max-product algorithm. We also show how different iteratively decodable channel codes fit very naturally into this picture. For loop-less factor graphs the summary-product algorithm gives back the desired results; for loopy factor graphs the results are only approximations to the desired ones. As we do not want that the summary-product algorithm becomes prohibitively computationally intense, we have to bound the local state space sizes. Under these circumstances, it seems favorable in our applications at hand to perform a sub-optimal algorithm on a loopy factor graph than to perform an optimal algorithm on a loop-less factor graph. One reason for this phenomenon lies in the fact that under the above restrictions much stronger codes can be achieved when allowing factor graphs with cycles than without cycles. ...
Product details
Binding:
Paperback
Edition:
1
Number of Pages:
246
Publisher:
Hartung-Gorre
Languages:
Published: English, Original: English
ISBN10:
3896498657
Weight:
454 g
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