LCD Codes and Iterative Decoding by Projections, a First Step Towards an Intuitive Description of Iterative Decoding
Jalal Etesami, Fangning Hu, Werner Henkel · 2011
From our earlier works, we know that in the case of analog codes, a Turbo-like iterative decoding can be nicely illustrated as iterative projections onto super codes that correspond to parts of the parity check matrix. So-called LCD (linear code with complementary dual) codes are recognized as a counterpart in finite fields for the orthogonal case, where two iterative projections lead to the final solution. A method for decomposing an arbitrary LCD code C into two super LCD codes C1and C2such that decoding by iteratively projecting the received vector onto C1and C2results in the same decoding solution as directly projecting the vector onto the original code space C. This is not necessarily a maximum-likelihood solution opposite to the analog case. A bound on the probability of finding the nearest codeword is provided.