Privacy security issues under the classic randomized response (RR) model proposed by Warner and its extended K-RR model are studied. Firstly, in order to provide references for the accuracy of the private distribution estimation problem under RR mechanism, the lower bounds of the differential privacy parameter and the number of participates are deduced for an accuracy objective of (α,δ)–accurate in statistics. Secondly, when the prior distribution is nonuniform, the data utility has a ceiling effect in the high privacy region by taking the prior into account. In this case, the average distortion, which is defined as the expected Hamming distance between the input and output data, is no longer feasible to measure the data utility. Motivated by this, the error probability is proposed as a measure of data utility for unifying different privacy metrics, where the error probability is defined to be the expected Hamming distance between the input and reconstructed data based on maximum a posteriori estimation. Thirdly, under a unified privacypreserving framework using RR mechanism based on error probability criterion, the relationship among differential privacy, identifiability privacy and mutual information privacy is established. Given a maximum allowable error probability Pmax E , the optimal privacy parameters of these three privacy notions are derived with full consideration of the prior distribution. Then, a Bayes-based utility function, which corresponds to the converse of the Bayes risk, is constructed to measure the degree of privacy leakage. Given a maximum allowable correct probability Pmax C , the accuracy objective of the statistical estimate is considered to derive the range of local differential privacy parameter from the perspective of security. Fourthly, all the research results above are further extended to K-RR mechanism, too. Finally, the correctness and effectiveness are further verified by simulation experiments. Results reveal that the error probability can be applied to any prior distribution case, while the average distortion criterion is only a special case with uniform distribution. Therefore, the error probability proposed in the paper is more reasonable to be used as a common criterion to measure the data utility for RR model so as to unify different privacy metrics.

A rate adaption scheme is given at the receiver using rateless codes and log‐likelihood ratio (LLR) threshold‐based adaptive demodulation (ADM). The received bits with LLR absolute values higher than the preset threshold are demodulated by the receiver, otherwise, deleted. Through the theoretical analysis of the average mutual information (MI) of the demodulated bits, the method is obtained to calculate the LLR demodulation threshold under the required error performance after decoding and the constraint of codeword length for decoding. Then, the rate adaption scheme is applied in a parallel multiple relay wireless communication system. The LLR threshold is set according to the instantaneous SNR of the received signals in order to keep the average MI per demodulated bit of each relay link the same. The demodulated bits coming from all links are combined for decoding. The 256‐QAM constellation and Raptor code are then considered as a special case to design a sample scheme. Simulation results prove the correctness of the theoretical analysis and the feasibility of the proposed scheme, and when it is employed by a multi‐relay transmission system, the diversity gain can be obtained, and the anti‐fading and the anti‐jamming abilities of the system are promoted.