Performance of Iterative Algebraic Decoding of Codes Defined on Graphs: An Initial Investigation

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.