Chaotic dynamics based apparatus and method for tracking through dropouts in symbolic dynamics digital communication signals

A predictive correction communication system comprising:

• a symbol encoder having
• means for storing at least 2N different trajectory interval data, each being on the same deterministic chaotic trajectory;
• means for receiving an externally generated N-bit sequence,
• means for selecting one of said 2N trajectory interval data based on said N-bit sequence, and for generating a state signal representing a segment of said deterministic chaotic trajectory defined by said trajectory data,
• means for transmitting a communication signal based on said state signal;
• and
• a predictive symbol receiver having means for estimating, based on a received communication signal over n bit periods, a future trajectory of said communication signal over a subsequent approximately N bit periods, where n<<N comprising
• means for generating a receiver state signal representing said deterministic chaotic trajectory, said means having a coupling means for initializing said receiver state signal to a state based on said communication signal in response to said communication signal being above a predetermined threshold for approximately n bit periods, and
• a symbol detector means for generating an estimate of said N-bit sequence based on the receiver state signal.

A communication system comprising:

• a transmitter chaotic oscillator means for generating an x(t) and y(t) signal, said x(t) and y(t) signal representing a two-dimensional projection of a first vector moving along a deterministic chaotic state trajectory in a state space;
• a transmitter dynamic control means for receiving an externally generated stream of symbols, and for arranging said into N-bit blocks, and for initializing said transmitter oscillator means to an x(t) and y(t) source state, said source state being an interval on said deterministic chaotic state trajectory from which said trajectory sequentially orbits within and transitions between a first and second quadrant of said two-dimensional projection, in an order corresponding to the symbol value sequence of the N-bit block;
• means for detecting and for generating a symbol transmit signal Xtrans(t) representing at least one of said x(t) and y(t);
• means for receiving said symbol transmit signal Xtrans(t) and for outputting a corresponding received signal Xrec(t);
• a receiver chaotic oscillator means for generating an x′(t) and y′(t) signal, said x′(t) and y′(t) signal representing a two-dimensional projection of a second vector moving along a deterministic chaotic state trajectory having a form substantially identical to the deterministic chaotic state trajectory of the transmitter oscillator means;
• means for coupling said receiver chaotic oscillator means to said Xrec(t) signal wherein, in response to said Xrec(t) signal being greater than a predetermined threshold, said x′(t) and y′(t) signals are converged to a synchronous relation with said x(t) and y(t) signals of the transmitter chaotic oscillator means;
• and
• a symbol recovery means for detecting which of a first and a second quadrant of said two-dimensional projection that said x′(t) and y′(t) are in, based on said x′(t) and y′(t) values, and for outputting a recovered symbol signal in response,
• whereby, due to the deterministic chaotic state trajectory of the receiver having a form substantially identical to the deterministic chaotic state trajectory of the transmitter oscillator means, after said Xrec(t) signal falls below said predetermined threshold said x′(t) and y′(t) signals continue to estimate said x(t) and y(t) signals for approximately N bit cycles, and said symbol recovery means continues to output a sequence of said recovered symbol signals for a approximately N cycles which estimates an N-bit block of said externally generated stream of symbols.

A method for communication comprising steps of:

• receiving an externally generated N-bit sequence;
• generating an oscillating state signal having a deterministic chaotic trajectory, and having an initial state on said deterministic chaotic trajectory where a subsequent N-cycle trajectory segment encodes the N-bit sequence;
• transmitting a communication signal based on said state signal;
• and
• estimating, based on a received communication signal over n bit periods, a future trajectory of said communication signal extending approximately N bit periods, where n<<N, said estimating comprising steps of
• generating a receiver state signal representing said deterministic chaotic trajectory, wherein said receiver state signal is initialized to a state based on said communication signal in response to said communication signal being above a predetermined threshold for approximately n bit periods, and
• generating an estimate of said N-bit sequence based on the receiver state signal.