lower-rate LDPC codes
Lower-rate means that the rate of information bits you get through is lower, so $(128,32)$ is lower-rate than $(128,64)$.


  Also, would using a lower-rate ldpc code combat well against deletions in the channel or just misread bits? 


Classically, codes like these do not help against deletion; they are designed to find flipped bits; which is much more usual in digital communication channels, where the receiver has a clock that keeps running. If you had to model a deletion channel in this framework, you'd just go ahead and assume a 50% BER for all bits following (and including) the deleted bit. You could probably derive some (probably Bernoulli) distribution of how many bits are deleted per word, and when they happen, and thus calculate how many additional bit errors your code needs to be able to correct.

There's no functionality in a LDPC to guess which bits were deleted; idealized, mathematically, you're just trying to stuff $\mathbb F^{128-N_{deleted}}$ vectors into a vector space with dimensionality ${128}$. That's a bit strange.

I'm sure there's awesome math extending certain classes of channel codes to do that well, but I'm not aware of those, and my guess is that they are very complex to understand.

That's why it's usually desirable to have channel coding come directly after the physical recovery of symbols, and not after some component tried to make sense of those (aside from soft decoding gains etc).