Finite-length scaling of non-binary (c, d) LDPC codes for the BEC

This paper provides a performance analysis of the regular (c, d) LDPC code ensemble of codelength n with parity-check matrices defined over the general linear group GL(2^m). The transmission is assumed to take place over the binary erasure channel with erasure probability ε. In this work, the scaling approximation of the block erasure rate is generalized to the non-binary case, and the scaling parameter α of the approximation is derived. The proposed estimation is then compared with numerical results, showing that it predicts well the slope of the block erasure rate vs. channel erasure probability.