Explore the groundbreaking research on LDPC codes achieving list decoding capacity in this 23-minute IEEE conference talk. Delve into error-correcting codes, list-decoding, and unique decoding concepts. Examine Gallager's Ensemble and its significance as the first studied family of LDPC codes. Understand the main results presented by researchers from CMU, Haifa, and Stanford universities, focusing on how list-decoding is a local property. Investigate local properties of random linear codes and consider open problems in the field. Gain valuable insights into this cutting-edge area of coding theory and its potential applications.