On decoding failure probabilities for linear block codes on the binary erasure channel

It has been claimed that the performance of a linear block code under iterative decoding on the binary erasure channel is determined by the stoppin gdistance, i.e., the size of hte smallest non-empty stopping set in the associated Tanner graph. Indeed, this is true from the perspective of code word retrieval. However, we show that with respect to the retrieval of just the information bits within the code word, the stopping distance may not be main performance indicator since the smallest non-empty stopping sets might not hit the information set of bits carrying the information for a fixed code with a fixed decoder.