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An Algorithm for the Estimation of the Minimum Distance of LDPC Codes

Massimiliano Laddomada, M. Mondin

Published Jan 1, 2005• 0 citations
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The evaluation of the minimum distance of low-density parity-check (LDPC) codes remains an open problem due to the rather large dimension of the parity check matrix H associated with any practical code. In this article, we propose an effective modification of the error impulse (EI) technique for estimation of the minimum distance of the LDPCs. The EI method is successfully applied to suboptimum decoding algorithms such as the iterative MAP decoding algorithm for turbo codes. We present novel modifications and extensions of this method to the suboptimum iterative sum-product algorithm for LDPCs. Simulation results validate the functionality of the proposed technique. Simulations focus on a particular class of LDPC codes, but our approach is general and applies to any LDPC code.

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To find the minimum distance computation of LDPC codes is a NP problem, there has been no simple way to obtain the minimum distance of LDPC codes because of the code length being very long. To provide a solution to deal with this hard problem, this paper develops an algorithm to estimate the weights and distance of LDPC codes based on generator matrices. The paper establishes the upper bounds of weights and distances of LDPC codes by using the vectors of generator matrices, which is different from the existed probabilistic search methods for the weights' and distances of LCPC codes. The proposed algorithm can greatly reduce the searching time of weights and distances. Applying the algorithm we can obtain some LDPC codes of great distances and being free girth 4. Simulations verify the algorithms to be valid.

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The evaluation of the minimum distance of low-density parity-check (LDPC) codes remains an open problem due to the rather large dimension of the parity check matrix H associated with any practical code. In this article, we propose an effective modification of the error impulse (EI) technique for estimation of the minimum distance of the LDPCs. The EI method is successfully applied to suboptimum decoding algorithms such as the iterative MAP decoding algorithm for turbo codes. We present novel modifications and extensions of this method to the suboptimum iterative sum-product algorithm for LDPCs. Simulation results validate the functionality of the proposed technique. Simulations focus on a particular class of LDPC codes, but our approach is general and applies to any LDPC code.
LDPC codes provide a lot of advantages,such as low complexity and excellent error-correcting performance.Thus they have been adopted as a channel coding scheme in OFDMA PHY layer of WiMAX802.16e standard.In this paper,we use the minimum distance and code weight distribution to study the performance of LDPC codes.The ANC algorithm is studied deeply and is used to calculate the minimum distance of LDPC codes.Estimation results verify the correctness of ANC algorithm,and also show the influence of the minimum distance and code weight distribution on the error-correcting perfor-mance of LDPC codes.The results provide a reference for selecting LDPC codes in practical design.
To find the minimum distance computation of LDPC codes is a NP problem, there has been no simple way to obtain the minimum distance of LDPC codes because of the code length being very long. To provide a solution to deal with this hard problem, this paper develops an algorithm to estimate the weights and distance of LDPC codes based on generator matrices. The paper establishes the upper bounds of weights and distances of LDPC codes by using the vectors of generator matrices, which is different from the existed probabilistic search methods for the weights' and distances of LCPC codes. The proposed algorithm can greatly reduce the searching time of weights and distances. Applying the algorithm we can obtain some LDPC codes of great distances and being free girth 4. Simulations verify the algorithms to be valid.