Generating Code Representations Suitable for Belief Propagation Decoding
We describe a method for transforming a generalized parity check (GPC) matrix representation of a block linear binary code into another GPC matrix representation of the same code. The output GPC matrix has some attractive features from the point of view of iterative decoding algorithms like belief propagation. In particular, the number of ones in each row is reduced, and there are no cycles of length four in the equivalent graphical representation of the code. We illustrate the method for toy examples including the Golay code, and also for a Euclidean Geometry (n=255,k=127) code. The decoding performance of the belief propagation algorithm using our new GPC matrices improves significantly when they are used on the binary erasure channel, but the results are mixed for the additive white Gaussian noise channel–for the Euclidean Geometry code, the performance still improves, but for the Golay code it deteriorates. to be published in the Proceedings of the 40th Annual Allerton Conference on Communications, Control, and Computing This work may not be copied or reproduced in whole or in part for any commercial purpose. Permission to copy in whole or in part without payment of fee is granted for nonprofit educational and research purposes provided that all such whole or partial copies include the following: a notice that such copying is by permission of Mitsubishi Electric Research Laboratories, Inc.; an acknowledgment of the authors and individual contributions to the work; and all applicable portions of the copyright notice. Copying, reproduction, or republishing for any other purpose shall require a license with payment of fee to Mitsubishi Electric Research Laboratories, Inc. All rights reserved. Copyright c ©Mitsubishi Electric Research Laboratories, Inc., 2002 201 Broadway, Cambridge, Massachusetts 02139