Tree-based construction of LDPC codes

We present a construction of LDPC codes that have minimum pseudocodeword weight equal to the minimum distance, and perform well with iterative decoding. The construction involves enumerating a d-regular tree for a fixed number of layers and employing a connection algorithm based on mutually orthogonal Latin squares to close the tree. Methods are presented for degrees d = p^s and d = p^s + 1, for p a prime, one of which includes the well-known finite-geometry-based LDPC codes