Linear Time Encoding of LDPC Codes
Lu Jin, José M. F. Moura · 2010
Abstract—In this paper, we propose a linear complexity encoding method for arbitrary LDPC codes. We start from a simple graph-based encoding method “label-and-decide. ” We prove that the “label-and-decide ” method is applicable to Tanner graphs with a hierarchical structure—pseudo-trees—and that the resulting encoding complexity is linear with the code block length. Next, we define a second type of Tanner graphs—the encoding stopping set. The encoding stopping set is encoded in linear complexity by a revised label-and-decide algorithm—the “label-decide-recompute.” Finally, we prove that any Tanner graph can be partitioned into encoding stopping sets and pseudo-trees. By encoding each encoding stopping set or pseudo-tree sequentially, we develop a linear complexity encoding method for general low-density parity-check (LDPC) codes where the encoding complexity is proved to be less than 4 1 M 1 (k 0 1), where M is the number of independent rows in the parity-check matrix and k represents the mean row weight of the parity-check matrix. Index Terms—Encoding stopping set, low-density parity-check (LDPC) codes, linear complexity encoding, pseudo-tree, Tanner graphs.