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Algebraic coding for iterative decoding

Pascal O. Vontobel

Published Jan 1, 2003• 13 citations
Publisher
DOI
10.3929/ethz-a-004567465

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We investigate iterative algebraic decoding of codes defined on graphs. Practical codes that can achieve the Shannon limit are codes defined on graphs with its associated iterative decoding algorithms. Yet, the complexity of these algorithms is high, especially for long codes that attain capacity. For the foreseeable future, algebraic decoding will still be a standard in industry. We aim to harness the power of iterative processes and the low complexity of algebraic techniques by decoding codes on graphs using iterative algebraic techniques. We study the performance of codes on graphs decoded with this method taking into account the case of undetected errors. More specifically, we examine the threshold under which decoding is successful for the BEC and the BSC and compare these with that of certain LDPC codes. Our initial investigation shows that although a significant loss of performance is incurred on the BEC when compared to belief propagation decoding, for transmission over the BSC the threshold value is somewhat close to belief propagation. Especially for high rate codes iterative algebraic decoding could have good performance while maintaining low decoding complexity.
We consider an iterative decoding algorithm by using algebraic decoding for non-binary codes. In the decoding algorithm, algebraic decoding are carried out with respect to successively chosen input words, called the search centers. We present a new method for selecting sequences of search centers of algebraic decoding. Over the AWGN channel using BPSK signaling, we show simulation results on the error performances of the iterative decoding algorithms whose search centers are given by the proposed method, abbreviated IAD, for Reed-Solomon codes. From the simulation results, IAD provides considerably better error performance than GMD and CGA decoding with the same number of iterations.