Joint Blind Reconstruction of the Cyclic Codes and Self-Synchronous Scramblers in a Noisy Environment

Reverse analysis of the intercepted signal to reconstruct the communication scheme used by the transmitter is a key problem in the non-cooperative context. In this paper, we propose a new algorithm for the joint blind reconstruction of the cyclic codes and self-synchronous scramblers directly using soft-decision sequences. First, we derive the conclusion that if the parity polynomial of the factor of the generator polynomial of the cyclic code and the feedback polynomial of the self-synchronous scrambler are multiplied, then the vector corresponding to the inverse polynomial of this product forms a parity-check relation with the row vector of the self-synchronously scrambled cyclic code bit matrix, which is constructed by the sequence of self-synchronously scrambled cyclic codes. To detect this parity-check relation, the concept of average parity-check probability (APCP) is defined, which uses the intercepted soft-decision sequence to measure the reliability of the parity-check relation. An optimal threshold based on the minimum error criterion is then derived. When the APCP is greater than this optimal threshold, the parity-check relation is considered to be detected, i.e., the corresponding irreducible polynomial is a factor of the generator polynomial of the cyclic code and the corresponding candidate feedback polynomial is the feedback polynomial of the self-synchronous scrambler. Therefore, the blind reconstruction problem in this paper is exactly equivalent to the hypothesis-testing problem. Simulation results show that the algorithm is more fault-tolerant than existing algorithms in noisy environments.