An adaptive, a variable code rate,can respond to channel changes promptly channel coding method is proposed,a discrete memoryless binary source sequence 𝑿 is transformed losslessly to make it capable of error checking. After the transformation, 𝑿 has variable and fixed code rates through weighted probability arithmetic coding. Compared with a fixed code rate, a variable code rate can respond to channel changes promptly and effectively improve the transmission performance, thereby being suitable for more complex communication environments. We prove that when the code length is long enough, the decoding error probability of the weighted probability arithmetic coding is 0 and the encoding rate can reach 1. When the symbols in the sequence 𝑿 are uniformly distributed, the transmission rate can reach the channel capacity. In an additive-white-Gaussian-noise channel binary-phase-shiftkeying signal simulation experiment, the error correction performances under various fixed code rates were compared. When the fixed code rate was 0.5 and the block error rate (BLER) was 10 −3 the weighted probability arithmetic coding improved by 0.37 dB compared to that obtained using Polar CA-SCL, and when BLER was 10 −5 , it improved by 0.48 dB. The algorithm can be widely used in communication systems, data storage, and other fields.

 X is a discrete memoryless binary source , Sequence X undergoes lossless transformation to satisfy the requirement â\euroœEach 1 is separated by one or more zeros“, ”Each 0 is separated by one or two 1s” or similar condition , These conditions are the decision conditions for error detection in channel transmission. A new channel coding method is proposed based on a weighted probability model for lossless coding , The encoding rate and encoding and decoding steps of different conversion methods are different , It is proved that the decoding error probability can reach 0 when the code length is long enough. In the simulation experiment of BPSK signal in AWGN channel, At 0.5 bit rate, the proposed method improves 1.1dB over Polar code when FER is 0.001, and 1.4dB over Polar code when FER is 0.0001.Â

In this paper, a brand-new hash algorithm is provided. The length of the hash value can be customized. It is theoretically proved that the hash collision limit can be reached. The algorithm can be applied flexibly, and it can be applied to digital signatures, document verification and other fields in the future.

In this paper a brand new channel error detection and correction method is provided. Artificially adding symbols to the source binary sequence makes the binary sequence present a regularity. The receiver can use this rule to implement error detection and correction. Since many redundant symbols are added, a weighted probability model lossless coding method is proposed in this paper to remove redundant information, and the reasons why Markov chains and conditional probabilities are not feasible are given. It is proven that the method in this paper can reach the channel capacity when the code length approaches infinity. It is shown experimentally that when the code rate is 1/2 in the BIAWGN channel, the method in this paper is superior to the polar code and LDPC code.

Image analysis and compression We usually use Fourier transform, DCT transform and wavelet transform. The image transformation method based on weighted probability model is the new method described in this paper. We reasoned iterative formula of binary sequence-weighted probability model transformation versus inverse transformation, The encoding method of binary sequence transformation and inverse transformation are constructed. In the image transformation and inverse transformation experiment, yielded large number of duplicate values in the transformed data, which is suitable for the construction of a new image compression method. The inverse transform can reconstruct the image effectively, and has the obvious image edge annotation effect. This method can be used in image compression, image edge detection, image sharpening and intelligent recognition.