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We prove that approximating the size of stopping and trapping sets in Tanner graphs of linear block codes, and more restrictively, the class of low-density parity-check (LDPC) codes, is NP-hard. The ramifications of our findings are that methods used for estimating the height of the error-floor of moderate- and long-length LDPC codes, based on stopping and trapping set enumeration, cannot provide...
This paper considers information-theoretic lower bounds on the graphical complexity of finite-length LDPC codes. It is assumed that the transmission of the codes takes place over a memoryless binary-input output-symmetric (MBIOS) channel, and the bounds are expressed as a function of the code performance and their achievable gap to capacity (either under ML decoding or any sub-optimal decoding algorithm)...
Nonbinary LDPC codes demonstrated excellent performance. However, how to reduce the decoding complexity for such codes without performance degradation is still a problem to be solved. In this paper, the bit-flipping method is introduced into the standard Fourier transform decoding algorithm for decoding nonbinary LDPC codes. Simulation results show that the proposed method gains better BER performance...
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