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(5) The improved Logistic map.
By Setting x n = z n +1)/2 and c=4, Eq. (4) is changed to the improved Logistic map within symmetrical region as below.
From the above Eq. (7), we can notice that the proposed chaotic sequence based on weighted processing is a special case of the improved Logistic map chaotic sequences.
Subsequently, Chinese scholars Wang and Hu put forward to a special Logistic map designated as the improved Logistic map [19] in order to distinguish from the traditional Logistic map.
Furthermore, a chaotic sequence using the improved Logistic map without any processing has the worst performance in balance because its balance coefficient is always more than 0.06 at various code length.
Generally, the one-dimensional discrete chaotic maps can be applied to generate pseudo-random sequences, that is to say a qualified initial value is selected firstly and then a decimal chaotic sequence of length N is formed after N iterations according to chaotic map, for instance, the Chebyshev map, Tent map, Bernoulli map, Logistic map, and improved Logistic map.
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In order to improve the balance in classical chaotic sequences, a novel ranging code is proposed in this paper and constructed by a series of the improved Logistic-map chaotic sequences with different initial values through weighted optimization, summation, and quantization.
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