A new decoder is proposed to decode the (24, 12, 8) binary extended golay code up to four errors. It consists of the conventional hard decoder for correcting up to three errors, the detection algorithm for four errors...
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A new decoder is proposed to decode the (24, 12, 8) binary extended golay code up to four errors. It consists of the conventional hard decoder for correcting up to three errors, the detection algorithm for four errors and the soft decoding for four errors. For a weight-4 error in a received 24-bit word, Method 1 or 2 is developed to determine all six possible error patterns. The emblematic probability value of each error pattern is then defined as the product of four individual bit-error probabilities corresponding to the locations of the four errors. The most likely one among these six error patterns is obtained by choosing the maximum of the emblematic probability values of all possible error patterns. Finally, simulation results of this decoder in additive white Gaussian noise show that at least 93% and 99% of weight-4 error patterns that occur are corrected if the two E(b)/N(o) ratios are greater than 2 and 5 dB, respectively. Consequently, the proposed method can achieve a better percentage of successful decoding for four errors at variable signal-to-noise ratios than Lu et al.'s algorithm in software. However, the speed of the method is slower than Lu et al.'s algorithm.
A simple high-speed decoding algorithm for the [24, 12, 8] extended golay code suitable for implementation in combinational circuits is described. The proposed decoding algorithm corrects all patterns of three or fewe...
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A simple high-speed decoding algorithm for the [24, 12, 8] extended golay code suitable for implementation in combinational circuits is described. The proposed decoding algorithm corrects all patterns of three or fewer errors and detects quadruple errors using the Turyn construction of the extended golay code. It is proved that the [24, 12, 8] golaycode can correct all patterns of three or fewer random errors as well as certain patterns of quadruple errors such as four-bit cyclic single-burst and two-dimensional burst errors.
This paper investigates the performance of ordered statistics decoding (OSD) of linear block codes with binary differential phase-shift-keying (2DPSK) transmission on frequency nonselective multipath channels. First, ...
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This paper investigates the performance of ordered statistics decoding (OSD) of linear block codes with binary differential phase-shift-keying (2DPSK) transmission on frequency nonselective multipath channels. First, the wireless channel is modeled as a frequency nonselective, slow fading environment without intersymbol interference, Second, block interleaving is embedded to decorrelate the successive received symbols so that the performance of OSD, designed essentially for memoryless channels, is retained, Third, we derive the log-likelihood ratio of received symbols based on 2DPSK modulation, Fourth, we derive the statistics of received symbols and the statistics of received symbols after ordering. Further, we analyze the system error performance for sufficient degree of interleaving. Specifically, we derive the asymptotic bit error rate (BER) of OSD at high SNRs using the First-order approximation. Finally, we conduct experiments at various channel characteristics and interleaving degrees for (128, 64, 22) extended BCH code and (24, 12, 8) extended golay code. Results show that the error performance improves tremendously with increased interleaving degree.
A multimedia DS-CDMA system using an ARQ reverse link for data transmission is proposed and analysed. The system capacity is evaluated for several error-detecting codes (EDCs) such as the Hamming codes, the golaycode...
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A multimedia DS-CDMA system using an ARQ reverse link for data transmission is proposed and analysed. The system capacity is evaluated for several error-detecting codes (EDCs) such as the Hamming codes, the golaycode, the extended golay code and two kinds of BCH codes. A simple new model based on the asymptotic gain for block and convolutional codes is proposed. Using this asymptotic gain model, analytical expressions for the system capacity are derived, which makes the system capacity evaluation easier and faster. The proposed system allows a greater number of data users by using mon powerful block EDCs, instead of the Hamming class. The convolutional code efficiency in this system is also discussed.
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