An algorithm for the computation of the minimum distance of LDPC codes

• DOI: 10.1002/ett.1091
• Publication Date: 2006-01-24T12:47:58Z
• Authors: Fred Daneshgaran; Massimiliano Ladd...; Marina Mondin
• Keywords: minimum distance; LDPC codes; 0508 media and communications; 05 social sciences; 620

AbstractThe 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 matrixHassociated with any practical code. In this article, we propose an effective modification of the error impulse (EI) technique for computation of the minimum distance of the LDPC codes. The EI method is successfully applied to sub‐optimum decoding algorithms such as the iterative MAP decoding algorithm for turbo codes. We present novel modifications and extensions of this method to the sub‐optimum iterative sum‐product algorithm for LDPC codes. The performance of LDPC codes may be limited by pseudo‐codewords. There are, however, cases when the LDPC decoder behaves as a maximum‐likelihood (ML) decoder. This is specially so for randomly constructed LDPC codes operating at medium to high SNR values. In such cases, estimation of the minimum distancedmusing the error‐impulse method can be useful to assess asymptotic performance. In short, apart from theoretical interest in achievabledm, the technique is useful in checking whether an LDPC code is poor by virtue of having a lowdm. But, if a code has a highdm, simulations would still be needed to assess real performance. Copyright © 2006 AEIT.