Sufficient conditions for a regular LDPC code better than an irregular LDPC code

Decoding performance of LDPC (Low-Density Parity-Check) codes is highly dependent on the degree distributions of the Tanner graphs which define the LDPC codes. We compare two LDPC code ensembles, one has a uniform degree distribution and the other a non-uniform one over a BEC (Binary Erasure Channel) and a BSC (Binary Symmetric Channel) thorough DE (Density Evolution). We then derive sufficient conditions on the erasure probability of a BEC and the error probability of a BSC, under which the LDPC code ensembles with uniform degree distributions outperform those with non-uniform degree distributions.