TITLE: Has error correction been "solved"?
QUESTION [20 upvotes]: I recently came across Dan Piponi's blog post An End to Coding Theory and it left me very confused. The relevant portion is:

But in the sixties Robert Gallager looked at generating random sparse syndrome matrices and found that the resulting codes, called Low Density Parity Check (LDPC) codes, were good in the sense that they allowed messages to be transmitted at rates near the optimum rate found by Shannon - the so-called Shannon limit. Unfortunately the computers of the day weren't up to the task of finding the most likely element of M from a given element of C. But now they are. We now have near-optimal error correcting codes and the design of these codes is ridiculously simply. There was no need to use exotic mathematics, random matrices are as good as almost anything else. The past forty years of coding theory has been, more or less, a useless excursion. Any further research in the area can only yield tiny improvements.

In summary, he states that the rate of LDPC codes is very near channel capacity—so near that further improvements would not be worth the while.
So, my question is: What does modern research in error-correcting codes entail? I noticed that Dan did not mention what channel the rate of LDPC codes approach the capacity of, so maybe there exist channels that LDPC codes don't work well on? What other directions does modern research in the field explore?

REPLY [2 votes]: Polar Codes, designed by Arikan, have definitely beaten LDPC codes, in terms of achieving cutoff rate at shorter blocklengths and comparable complexity. See Arikan's 2019 IEEE Information Theory society Shannon Lecture (video, as well as paper on arxiv) in July 2019 in Paris [plot at 40:10 of the video], after he was awarded the Shannon award.
He presented "hot off the press" results in the Shannon lecture, which indicated that the new ensemble of "polarization-adjusted convolutional" codes which are a kind of concatenated codes (section VII of the paper) approach the dispersion lower bound for the cutoff rate, beating LDPC codes at a length of 128 bits [to my knowledge LDPC codes need a few thousand bits to do this].