In DGGE analysis Shannon index works on binary data. In my case, some of the distinct bands turn out representing the same identical bacterial species after sequencing.
not sure if I understand your question correctly. The Shannon Wiener Diversity Index does not work with binary data. In your case I guess you would use something link the band intensity (=abundance) to calculate the SWDI. If it turns out that some species have multiple patterns, then I'd suggest to simply combine their abundance - given that your analysis is carried out at species level.
If your using 16s rDNA gene as phylogenetic marker then it may be possible that same organism can show different banding pattern due to 16s is multicopy gene, may be any single base pair mutation in gene may show two different organism can show two same bands or even two same bacteria can show different bands .
In question I could not find any thing about 16S rDNA gene. Additionally there are always certain assumptions with any technique. When sample numbers are very high it could be used for removing similar profile samples. Technique is good but not perfect for community analysis.