Abstract: Vectors are quantized by representing the vectors by quantized values using a codebook having granular regions which are based on a coset code, and which lie inside a boundary region which is based on another coset code, the boundary region being other than an N-cube and other than the Voronoi region of a sublattice .LAMBDA..sub.b =M.LAMBDA..sub.g of a lattic .LAMBDA..sub.g upon which the granular regions may have been based.

Abstract: In general the invention features mapping a digital data sequence into a signal point sequence for data transmission over a channel characterized by a non-ideal response, by selecting the signal point sequence from a subset of all possible signal point sequences based on the digital data sequence and upon the response, all possible signal point sequences in the subset lying in a fundamental region of a filtered trellis code, the fundamental region being other than a simple Cartesian product of finite-dimensional regions.

Abstract: A digital data sequence is mapped into a signal point sequence for transmission, by selecting the signal point sequence from a subset of all possible signal point sequences based on the digital data sequence, all possible signal point sequences in the subset lying in a fundamental region of a trellis code, the fundamental region being other than a simple Cartesian product of finite-dimensional regions. In another aspect, a digital data sequence is mapped into a sequence of signal points for transmission, by specifying a class of possible sequences based on the digital data, and selecting the signal point sequence from the class, the selection being based on the respective average powers of the possible sequences of the class, the selection being based on not only a fixed-length block of the digital data.

Abstract: A modem for receiving data sent from a remote device over a communication channel by using a single carrier modulated signal, the modem including a receiver for receiving the modulated signal and for receiving a line probing signal sent by the remote device over the channel, the receiver being capable of receiving the modulated signal over any one of a plurality of frequency bands; a line probing processor for measuring characteristics of the channel based upon the received line probing signal; and a selector for selecting one of the plurality of frequency bands, said selection being based upon the measured characteristics of the channel, said selected frequency band to be used for receiving the modulated signal from the remote device.

Abstract: Apparatus for generating a (running digital sum) sequence of digital signals X.sub.k and/or a (partial response coded) sequence of digital signals Y.sub.k, K=1, 2, . . . , such that Y.sub.k =X.sub.k .+-.X.sub.k-l, L and integer, in which the Y.sub.x signals are a sequence in a given modulation code. In one aspect, the signals Y.sub.k are chosen to be congruent to coset representatives specified in accordance with a modulation code, a plurality of code constellations are used, and at least one constellation includes both a point with a positive sum of coordinates and one with a negative sum of coordinates. In another aspect, the signals X.sub.k are chosen to be congruent to a sequence of alternate (precoded) coset representatives. In other aspects, the Y.sub.k alphabet signals are evenly spaced, and a selectable, e.g., an optimal, tradeoff between S.sub.x and S.sub.y is made. An N-dimentional modulation code is generated as a sequence of one-dimensional signals.

Abstract: In a communication system, the combined advantages of decision feedback equalization and delayed decoding are achieved in a receiver by interleaving the signal points at the transmitter, and deinterleaving them at the receiver so that sufficiently reliable delayed decoder decisions can be used in estimating the distortion component of the received signal presently being processed in the decision feedback circuit.

Abstract: The unknown time when a transition in a signal point sequence has occurred is determined by a trellis technique based on known subsequences of symbols that preceded and followed the transition.

Abstract: A receiver for deciding which signal points were sent from a transmitter based on corresponding noise affected signals received via a distorting channel, the noise affected signals carrying information about a particular sequence of encoding states occupied in a succession of time intervals by a finite state process having a finite number of possible encoding states, the receiver including modifying circuitry for generating a plurality of different modified versions of each received signal, and a decoder for deciding which signal points were sent based on estimating a particular sequence of decoder states by storing a number of path histories of previous signal points and using the modified versions to extend the path histories, the different modified versions of each received signal numbering fewer than the number of stored path histories.