We present a tree-based construction of LDPC codes that have minimum
pseudocodeword weight equal to or almost 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 permutations or mutually orthogonal Latin squares to close
the tree. Methods are presented for degrees d=ps and d=ps+1, for p a
prime. One class corresponds to the well-known finite-geometry and finite
generalized quadrangle LDPC codes; the other codes presented are new. We also
present some bounds on pseudocodeword weight for p-ary LDPC codes. Treating
these codes as p-ary LDPC codes rather than binary LDPC codes improves their
rates, minimum distances, and pseudocodeword weights, thereby giving a new
importance to the finite geometry LDPC codes where p>2.Comment: Submitted to Transactions on Information Theory. Submitted: Oct. 1,
2005; Revised: May 1, 2006, Nov. 25, 200