Encoding

This page describes the encoding challenge of LDPC codes

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Even though the parity check matrix of an LDPC code is sparse, the same does not generally hold for the generator matrix $G$. Correspondingly, encoding via matrix multiplication, i.e., via $c=uG$, incurs a computational cost of $\mathcal{O}(n^2)$.

Better solutions with faster encoding were found by encoding using the parity check matrix itself, using back substitution algorithms. A well cited work on this is the work by Richardson, T.J. and Urbanke, R.L.. Alternatively, a more compact solution (around the same lines) which is limited to IEEE802.11 LDPC codes can be found here.