On threshold prediction of low-density parity-check codes with structure

Low-density parity-check (LDPC) codes based on structured parity check matrices are widely used due to their favorable implementation properties. Often, however, the convergence threshold is optimized based on the general LDPC code ensemble (i.e., the degree profile only) without taking into account the imposed structure, leading to a mismatch of anticipated and actual threshold performance. In this paper, we study this mismatch in more detail and restrict ourselves to the simplest yet most popular constraint: the dual-diagonal structure of the parity-check matrix of a repeat-accumulate code, enabling linear-time encoding. We show that convergence threshold predictions based on density evolution (DE) or EXIT charts need an appropriate choice of component code models. We quantify the threshold prediction error for both BEC and AWGN channels over a wide range of code rates and degree profile optimization techniques. Finally, we provide an explicit example illustrating the achievable gains by using properly designed degree profiles.