We present a new soft-decision majority decoding algorithm for Reed-Muller codes RM (r, m). First, the reliabilities of 2(m) transmitted symbols are recalculated into the reliabilities of 2(m-r) parity checks that rep...
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We present a new soft-decision majority decoding algorithm for Reed-Muller codes RM (r, m). First, the reliabilities of 2(m) transmitted symbols are recalculated into the reliabilities of 2(m-r) parity checks that represent each information bit. In turn, information bits are obtained by the weighted majority that gives more weight to more reliable parity checks. It is proven that for long low-rate codes RM (r, m),our soft-decision algorithm outperforms its conventional hard-decision counterpart by 10 log(10)(pi/2) approximate to 2 dB at any given output error probability. For fixed code rate R and m --> infinity our algorithm increases almost 2(r/2) times the correcting capability of soft-decision bounded distance decoding.
Error exponents are studied for recursive and majority decoding of general Reed-Muller (RM) codes RM(r, m) used on the additive white Gaussian noise (AWGN) channels. Both algorithms have low complexity and correct man...
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Error exponents are studied for recursive and majority decoding of general Reed-Muller (RM) codes RM(r, m) used on the additive white Gaussian noise (AWGN) channels. Both algorithms have low complexity and correct many error patterns whose weight exceeds half the code distance. decoding consists of multiple consecutive steps, which repeatedly recalculate the input symbols and determine different information symbols using soft-decision majority voting. For any code RM(r, m), we estimate the probabilities of the information symbols obtained in these recalculations and derive the analytical upper bounds for the block error rates of the recursive and majority decoding. In the case of a low noise, we also obtain the lower bounds and show that the upper bounds are tight. For a higher noise, these bounds closely approach our simulation results.
An asynchronous secure communication scheme of modulation of message on optical chaos, combining (6, 3) linear block codes (LBC) with majority decoding, is proposed. In this scheme, a semiconductor laser (SL) with ele...
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An asynchronous secure communication scheme of modulation of message on optical chaos, combining (6, 3) linear block codes (LBC) with majority decoding, is proposed. In this scheme, a semiconductor laser (SL) with electro-optical phase feedback is used to generate an optical chaotic carrier with high complexity. We calculate the sum of the absolute values at adjacent three moments in the chaotic sequence, and divide interval between its maximum and minimum into eight different segments, which are used as the key for generating a new chaotic sequence according to a certain rule. Introducing (6, 3) LBC to encode the message, and using dispersion-compensating fiber (DCF) to eliminate the effect of dispersion induced by single mode fiber (SMF), and then using majority decoding to demodulate the original message at receiving end, we demonstrate that the performance of the bit error rate (BER) in a channel with noise is well improved, and the distortion is greatly reduced. Moreover, our system can realize communication between transmitter and receiver without chaotic synchronization by negotiating these keys through a secret channel.
Some binary linear codes of length 50 and 100 are constructed using the adjacency matrices of the Hoffman-Singleton graph and the Higman-Sims graph. Some of the codes are optimal or nearly optimal for the given length...
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Some binary linear codes of length 50 and 100 are constructed using the adjacency matrices of the Hoffman-Singleton graph and the Higman-Sims graph. Some of the codes are optimal or nearly optimal for the given length and dimension. The dual codes admit majority logic decoding.
When creating new technical solutions it's necessary to ensure the technical parameters which set cost is the lowest. It's advisable to use the principle of minimum costs and restrictions on the technical effe...
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ISBN:
(纸本)9781538643402
When creating new technical solutions it's necessary to ensure the technical parameters which set cost is the lowest. It's advisable to use the principle of minimum costs and restrictions on the technical effect, as well as the external and internal parameters that characterize the information protection system errors. The methodological basis for solving optimization problems is also the theory of operations research. Since the system is created to protect information from error, providing the required noise immunity value of the indicator at minimum cost, the performance indicator of permissible projects may be instrumental in the creation of processing costs reliability of the device. The problem of optimal mathematical programming is reduced to finding the number of repetitions of the function argument values of the message and the likelihood of distortion of a single character codeword, which minimize the functional, and can be solved by a classical method of Lagrange multipliers.
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