25. A system comprising: a communication channel operably connected to a first communication device and a second communication device; the first communication device, which includes a speech encoder, which processes an input speech signal, resulting in a compressed encoder representation of the input speech signal, a speech recognizer, and a difference encoder, which determines a compressed recognizer representation of a corresponding dictionary speech element that approximates the input speech signal when the speech recognizer identifies the corresponding dictionary speech element, calculates one or more differences between the compressed encoder representation and the compressed recognizer representation, and compiles compressed speech information that includes representations of the one or more differences; wherein the first communication device further includes a transmitter, which transmits the compressed speech information that includes representations of the one or more differences when the speech recognizer identifies the corresponding dictionary speech element and transmits the compressed encoder representation of the input speech signal when the speech recognizer does not identify a dictionary speech element that approximates the input speech signal; and wherein the system further comprises the second communication device, which constructs an output speech signal based on the compressed speech information, and information associated with the corresponding dictionary speech element, and the compressed encoder information.
25. A system comprising: a communication channel operably connected to a first communication device and a second communication device; the first communication device, which includes a speech encoder, which processes an input speech signal, resulting in a compressed encoder representation of the input speech signal, a speech recognizer, and a difference encoder, which determines a compressed recognizer representation of a corresponding dictionary speech element that approximates the input speech signal when the speech recognizer identifies the corresponding dictionary speech element, calculates one or more differences between the compressed encoder representation and the compressed recognizer representation, and compiles compressed speech information that includes representations of the one or more differences; wherein the first communication device further includes a transmitter, which transmits the compressed speech information that includes representations of the one or more differences when the speech recognizer identifies the corresponding dictionary speech element and transmits the compressed encoder representation of the input speech signal when the speech recognizer does not identify a dictionary speech element that approximates the input speech signal; and wherein the system further comprises the second communication device, which constructs an output speech signal based on the compressed speech information, and information associated with the corresponding dictionary speech element, and the compressed encoder information. 26. The system of claim 25 , wherein the communication channel is a wireless communication channel, and the first device further includes a dipole antenna for sending the compressed speech information over the wireless communication channel.