Complexity-constrained spatially coupled LDPC codes based on protographs

Spatially coupled low-density parity-check (SC-LDPC) codes are often thought as codes with very long block lengths. However, they can be decoded through sliding window (SW) decoders achieving near-optimal performance when the window size is a few times larger than the code syndrome former constraint length. This makes SC-LDPC codes with short constraint length suitable for low-latency transmissions, and they can even outperform their block code counterparts. Complexity of SW decoders increases linearly with the window size and with the number of decoding iterations. When complexity is constrained, an optimal trade-off between the window size and the maximum number of decoding iterations has to be found. In this paper, we propose a PEXIT-based method to find the best trade-off for codes with short syndrome former constraint length. We consider codes based on protographs, and validate the results of the PEXIT-based method through Monte Carlo simulations.