New Decoding Algorithm for Cryptcodes Based on Quasigroups for Transmission Through a Low Noise Channel

Abstract

Random Codes Based on Quasigroups (RCBQ) are cryptcodes, so they provide (in one algorithm) a correction of certain amount of errors in the input data and an information security. Cut-Decoding and 4-Sets-Cut-Decoding algorithms are proposed elsewhere and they improve decoding of these codes. In the decoding process of these codes, three types of errors appear: more-candidate-error, null-error and undetected-error. More-candidate-errors can occur even all bits in the message are correctly transmitted. So, the packet-error (and bit-error) probability can be positive for very small bit-error probability in the noise channel. In order to eliminate this problem, here we define new decoding algorithms (called Fast-Cut-Decoding and Fast-4-Sets-Cut-Decoding algorithms) that enable more efficient and faster decoding, especially for transmission through a low noise channel. We present several experimental results obtained with these new algorithms. Also, we analyze the results for bit-error and packet-error probabilities and decoding speed when messages are transmitted through Gaussian channel with different values of signal-to-noise ratio (SNR).