Error Performance Prediction of Randomly Shortened and Punctured LDPC Codes

In this contribution, we show that the word error rate (WER) performance in the waterfall region of a randomly shortened and punctured low density parity check code can be accurately predicted from the WER performance of its finite-length mother code. We derive an approximate analytical expression for the mutual information (MI) required by a daughter code to achieve a given WER, based on the MI required by the mother code, which shows that the gap to the capacity of the daughter code grows the more the code is punctured or shortened. The theoretical results are confirmed by simulations (where the random shortening and puncturing pattern is either selected independently per codeword or kept the same for all codewords) for practical codes on both the binary erasure channel and the binary-input additive white Gaussian noise channel.