Abstract: An apparatus and method for echo cancellation that detects and tracks the active regions of the echo channel impulse response rather than the entire echo channel impulse response and uses this sparse model to cancel the echo component of the received signal. Two sets of filter coefficients are used, one to remove and track the active regions and one to detect the active regions.

Abstract: A system, device, and method for time-domain equalizer training uses a two-pass auto-regressive moving average model. A communication channel is first modeled using p1 poles and q1 zeros to form a first shortened channel impulse response having a first approximation H1(z)=B1(z)/1+A1(z), wherein q1, is greater than a predetermined cyclic prefix length. A time-mirrored image of the first shortened channel impulse response is then formed, and the resulting time-mirrored image of the first shortened channel impulse response is modeled using p2 poles and q2 zeros to form a second shortened channel impulse response having a second approximation H2(z)=B2(z)/1+A2(z), wherein q2 is less than or equal to the predetermined cyclic prefix length. The time-domain equalizer coefficients are determined by combining A1(z) and A2(1/z) with an appropriate amount of delay.

Abstract: An apparatus and method for echo cancellation that detects and tracks the active regions of the echo channel impulse response rather than the entire echo channel impulse response and uses this sparse model to cancel the echo component of the received signal. Two sets of filter coefficients are used, one to remove and track the active regions and one to detect the active regions.

Abstract: A higher code rate Low-Density Parity Check (LDPC) matrix may be designed by concatenating additional matrices to a ?-rotation parity check matrix. The concatenated matrix may be selected such that the resultant LDPC matrix exhibits good expansion characteristics to enable the LDPC matrix to be used with variable block length codes. The codes may be designed by generating an ensemble of available codes, encoding them with information vectors of weight 1 and 2 and discarding codes with a low minimum distance. The approximate upper bounds for the remaining codes are then calculated and a small set of codes with the lowest bound under high signal to noise ratio is selected. The girth distributions for the remaining codes are then calculated and the code that has the minimum number of short cycles is selected. The selected code is concatenated to the original v-rotation parity check matrix.

Abstract: A method and apparatus for establishing communication between a sending facsimile machine and a receiving facsimile machine first receives an answer tone message for a specified time. It then is determined if a given joint menu message has been received from the receiving facsimile machine at any time during the specified time. If it is determined that the given joint menu message has not been received from the receiving facsimile machine at any time during the specified time, then the above noted alias joint menu message is forwarded to the sending facsimile machine. The alias joint menu message is different from the given joint menu signal and thus, not a true joint menu message that can be used by the sending facsimile machine.

Abstract: A system, device, and method for determining the sampling time for a time-domain equalizer divides an over-sampled sequence into a plurality of individual Nyquist rate sequences, determines time-domain equalizer coefficients using one of the individual Nyquist rate sequences, and measures the performance for all individual Nyquist rate sequences using the time-domain equalizer coefficients. The Nyquist rate sequence having the best performance is selected, and the sampling time (delay) is configured so that the selected Nyquist rate sequence is provided to the time-domain equalizer.

Abstract: A system, device, and method for time-domain equalizer (TEQ) training determines the TEQ order and TEQ coefficients by applying the multichannel Levinson algorithm for auto-regressive moving average (ARMA) modeling of the channel impulse response. Specifically, the TEQ is trained based upon a received training signal. The received training signal and knowledge of the transmitted training signal are used to derive an autocorrelation matrix that is used in formulating the multichannel ARMA model. The parameters of the multichannel ARMA model are estimated via a recursive procedure using the multichannel Levinson algorithm. Starting from a sufficiently high-order model with a fixed pole-zero difference, the TEQ coefficients corresponding to a low-order model are derived from those of a high-order model.