Does the performance of LDPC code $C$ depends on the covering radius, $Cr(C)$?
The performance of $LDPC$ code $C$ depends on a lot of parameters as like as: 1) regularity or irregularity 2) stopping set 3) the channel for simulation ($BSC$ or $AWGN$ channel or others) 4) the decoding algorithm 5) rate and minimum distance of code and some new parameters that introduced in many paper with this subject. Also you can see a paper with name "Does the performance of $LDPC$ codes depend on channels?"
But in general, this question isn't solve completely. I think in iterative decoding, the covering radius is not so important. We have $LDPS$ codes with large covering radius that has very good performance and also we have $LDPC$ codes with small covering radius that has good performance. The covering radius is very important parameter in source coding as like as compression. In channel coding, it is not so important.