Systems and methods for system identification, encoding and decoding signals in a non-linear system are disclosed. An exemplary method can include receiving the one or more input signals and performing dendritic processing on the input signals. The method can also encode the output of the dendritic processing of the input signals, at a neuron, to provide encoded signals.
Please help me write a proper abstract based on the patent claims. CLAIM: 1. A method of encoding one or more input signals in a non-linear system, comprising: receiving the one or more input signals; performing non-linear dendritic processing on the one or more signals to provide a first output; providing the first output to one or more neurons; and encoding the first output, at the one or more neurons, to provide one or more encoded signals. 2. The method of claim 1, wherein the receiving further comprises modeling the one or more input signals. 3. The method of claim 2, wherein the modeling further comprises modeling the one or more input signals using Volterra series. 4. The method of claim 1, further comprising: modeling the one or more input signals into one or more spaces; performing dendritic processing on each of the one or more spaces to provide an output; and adding the output from dendritic processing of each of the one or more orders to provide a first output. 5. A method of decoding one or more encoded signals in a non-linear system, comprising: receiving the one or more encoded signals; performing convex optimization on the one or more encoded signals to produce a coefficient; and constructing one or more output signals using the coefficient. 6. The method of claim 5, wherein the performing comprises: determining a sampling matrix using the one or more encoded signals; determining a measurement using a time of the one or more encoded signals; and determining a coefficient using the sample matrix and the measurement. 7. The method of claim 5, wherein the constructing the one or more output signals further comprises: determining a bias based on the one or more encoded signals; and determining the one or more output signals based on the bias and the coefficient. 8. The method of claim 5, wherein the receiving further comprises modeling the one or more encoded signals. 9. The method of claim 8, wherein the modeling further comprises modeling using Volterra series. 10. The method of claim 5, further comprising: modeling the one or more encoded signals into one or more orders; and performing convex optimization on each of the one or more orders to provide the coefficient for each of the one or orders. 11. A method of identifying a projection of an unknown dendritic processor in a non-linear system, comprising: receiving a known input signal; processing the known input signal using a projection of the unknown dendritic processor to produce a first output; encoding the first output, using a neuron, to produce an output signal; and comparing the known input signal and the output signal to identify the projection of the unknown dendritic processor. 12. The method of claim 11, wherein the receiving further comprises modeling the known input signal. 13. The method of claim 12, wherein the modeling further comprises modeling the known input signal using Volterra series. 14. The method of claim 11, further comprising: modeling the known input signal into first one or more orders; and modeling the projection of the dendritic processor of the channel into second one or more orders. 15. The method of claim 14, for each of the first one or more orders: processing the projection of each of the second one or more orders using the known input signal to produce a first output; and adding the output from dendritic processing of each of the one or more orders to provide a first output. 16. A system for encoding one or more input signals, comprising: a first computing device having a processor and a memory thereon for the storage of executable instructions and data, wherein the instructions are executed to: receiving the one or more input signals; performing dendritic processing on the one or more signals to provide a first output; providing the first output to one or more neurons; and encoding the first output, at the one or more neurons, to provide one or more encoded signals. 17. The system of claim 16, wherein the receiving further comprises modeling the one or more input signals. 18. The system of claim 17, wherein the modeling further comprises modeling the one or more input signals using Volterra series. 19. The system of claim 16, further comprising: modeling the one or more input signals into one or more orders; performing dendritic processing on each of the one or more orders to provide an output; and adding the output from dendritic processing of each of the one or more orders to provide a first output. 20. The system of claim 16, further comprising: providing the one or more encoded signals to a decoder for decoding the one or more output signals.