  We investigate the reasons behind the superior performance of belief
propagation decoding of non-binary LDPC codes over their binary images when the
transmission occurs over the binary erasure channel. We show that although
decoding over the binary image has lower complexity, it has worse performance
owing to its larger number of stopping sets relative to the original non-binary
code. We propose a method to find redundant parity-checks of the binary image
that eliminate these additional stopping sets, so that we achieve performance
comparable to that of the original non-binary LDPC code with lower decoding
complexity.
