This paper describes a combinatorial approach to estimate the error rate performance of low-density parity-check (LDPC) codes decoded by (quantized) soft-decision iterative decoding algorithms. The method is based on efficient enumeration of input vectors with small distances to a reference vector whose elements are selected to be the most reliable values from the input alphabet. Several techniques, including modified cycle enumeration, and the efficient derivation of problematic inputs for finer quantizers from those of coarser ones are employed to reduce the complexity of the enumeration. The error rate estimate is derived by testing the input vectors of small distances followed by estimating the contribution of larger distance vectors. We demonstrate by a number of examples that the proposed method provides accurate estimates of error rate with computational complexity much lower than that of Monte Carlo simulations, especially at the error floor region.

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Keywords error floor, error rate estimation, finite-length LDPC codes, iterative decoding, Low-density parity-check (LDPC) codes, quantization, soft-decision decoding algorithms
Persistent URL
Journal IEEE Transactions on Communications
Xiao, H. (Hua), Banihashemi, A, & Karimi, M. (Mehdi). (2013). Error rate estimation of low-density parity-check codes decoded by quantized soft-decision iterative algorithms. IEEE Transactions on Communications, 61(2), 474–484. doi:10.1109/TCOMM.2012.122112.110805