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Linear Time Encoding of LDPC Codes

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2 Author(s)
Jin Lu ; Sun Microsyst., Bloomfield, CO, USA ; Moura, J.M.F.

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 ·M ·((k¿- 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.

Published in:

Information Theory, IEEE Transactions on  (Volume:56 ,  Issue: 1 )

Date of Publication:

Jan. 2010

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