Channel adaptive error-detecting codes with guaranteed residual error probability

A method for checking a signal transmission of a specified message with a number of d bits from a sender to a receiver by a control unit such that a speed at which a residual error probability is calculated and an accuracy of the calculated residual error probability utilizing a linear block code created via a coding tool, a channel model, and a linear feedback shift register are increased, the method comprising:

• describing the channel model via a characterizing Markov-modulated Bernoulli process;
• performing an iterative first calculation of probability values for a probability distribution of states of one of the d bits relative to a current bit after transmission of a signal by a signal transmission unit, starting from a current probability distribution of states in the current bit, taking into account all possible transitions that result from a Cartesian product of a number of states in accordance with the Markov-modulated Bernoulli process and the number of states of the linear feedback shift register, the control unit adding probability values of transitions into an equal state and performing this iteration up to a probability distribution of a final bit;
• performing an iterative second calculation of probability values for the probability distribution of the states of one of the d bits relative to the current bit after transmission of the signal by the signal transmission unit, starting from the current probability distribution of the states in the current bit, ignoring all transitions obtained during a specified zero state, the control unit adding the probability values of transitions into an equal state and performing this iteration up to the probability distribution of the final bit;
• and
• forming a difference from the probability values of a specified zero state obtained during the first iterative calculation with the probability values of the specified zero state obtained during the second iterative calculation, as the residual error probability having the increased accuracy.