Efficient use of a hybrid decoding technique for LDPC codes
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Efficient use of a hybrid decoding technique for LDPC codes Walter Prado de Souza Guimarães1* , José S Lemos-Neto2 and Valdemar C da Rocha Jr2 Abstract A word error rate (WER) reducing approach for a hybrid iterative error and erasure decoding algorithm for low-density parity-check codes is described. A lower WER is achieved when the maximum number of iterations of the min-sum belief propagation decoder stage is set to certain specific values which are code dependent. By proper choice of decoder parameters, this approach reduces WER by about 2 orders of magnitude for an equivalent decoding complexity. Computer simulation results are given for the efficient use of this hybrid decoding technique in the presence of additive white Gaussian noise. Keywords: Iterative decoding; LDPC codes; Erasure decoding
Introduction Low-density parity-check (LDPC) codes were first introduced by Gallager in 1963 [1] and rediscovered by Mackay [2] in late 1990s. LDPC codes are characterized by a sparse parity-check matrix H, for which an iterative decoder becomes an attractive option. One example is the belief propagation (BP) decoder which achieves the optimal MAP (Maximum a Posteriori) decoding condition if the code graph does not contain cycles ([3], p. 211). However, most LDPC codes have cycles in their Tanner graph representation, mainly for small and medium blocklengths [4], which adversely affect code performance. The BP decoding operation is executed for a preset number of iterations, and in case of a decoding failure, it leads to a frame error which implies a number of bits erroneously decoded. In the error-floor region, where LDPC codes exhibit a sudden saturation in word error rate (WER) for a sufficiently high signal-to-noise ratio (SNR), the bit errors are primarily caused by trapping sets ([3], p. 225). A considerable amount of research has gone into designing decoders to mitigate the errors caused by trapping sets [4-6]. In [7], a bi-mode decoder for LDPC codes was proposed for the additive white Gaussian noise (AWGN) channel, called a hybrid decoder (HD). The HD system operates in two modes (stages), where in mode 1 (first *Correspondence: [email protected] 1 Department of Electronics and Communications, State University of Amazonas, Manaus 69050-020, Brazil Full list of author information is available at the end of the article
stage) a min-sum BP decoding is employed and in mode 2 (second stage) an iterative erasure decoder is used. One cycle of the HD operation includes at least one passage through the min-sum BP decoder, and if necessary, it also includes a passage through the erasure decoder. In this article, we make a more efficient use of the HD system introduced in [7]. In comparison with [7], the novelty here is the experimental determination of appropriate values for the number of iterations for the min-sum BP decoder which permits to perform a fine tune on the HD system. Furthermore, a new material has been added to explain the estimation of the number of bits to be erased at
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