Linear Time Encoding of LDPC Codes

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 (k0 1), where M is the number of independent rows in the parit...

• Type: Journal
• Year: 2008
• Where: CORR
• Authors: Jin Lu, José M. F. Moura
• Keywords: CORR 2008, Education, Linear Complexity, Simple Graph-based Encoding, Tanner Graph