Abstract: A sixty-four state convolutional code known as the "Cole code" is disclosed and take systematic and non-systematic forms. The state variables of the Cole code are r(n-1), r(n-2), s(n-1), s(n-2), p(n-1), and x(n-1). In the four-to-five non-systematic form, four inputs p(n), q(n), r(n) and s(n) are used to generate five outputs y.sub.4 (n), y.sub.3 (n), y.sub.2 (n), y.sub.1 (n), and y.sub.0 (n) according to: y.sub.4 (n)=q(n); y.sub.3 (n)=p(n)+r(n)r(n-1)+r(n-2)+r(n-1)s(n)+r(n-1)s(n-2); y.sub.2 (n)=r(n-1)+s(n)+s(n-2); y.sub.1 (n)=r(n)+r(n-1)r(n-2)+p(n-1)+p(n-2)+q(n-1); and y.sub.0 (n)=s(n-1), where p(n-2)+q(n-1)=x(n-1). New state variables are obtained directly from the inputs and from the previous state variables, except for x(n) which is equals q(n)+p(n-1). In a three-to-four non-systematic implementation of the Cole code, q(n) is not input, y.sub.4 is not output, and q(n-1) is set equal to zero. In the four-to-five systematic form of the Cole code, the inputs y.sub.4, y.sub.3, y.sub.2, y.sub.

Abstract: A modem is provided with a Trellis encoder which utilizes a double-branch feedback, with a first branch of the feedback including a convolutional encoder, and a second branch of the feedback including a parity generator which computes the parity of consecutive offsets. The Trellis encoder includes a four-dimensional (4D) mapper which generates pairs of 2D points u(k). Each point is offset by a value c(k) to obtain offset points y(k) which are then predistorted by a value p(k) to obtain an output x(k). The output x(k) is filtered to update the predistortion value p(k) which in turn is used to update the offset value c(k). The offset value c(k) is chosen from a 2D constellation lattice which is closest to the predistortion value p(k). The parity C0 of consecutive offset values c(k) is used in conjunction with a redundant bit output Y0 of a convolutional encoder to generate a rotational feedback bit input U0 to the 4D mapper, where the rotational bit input is the parity of two 2D points chosen by the mapper.

Abstract: Apparatus and methods in both modem transmitters and receivers are provided for accommodating secondary channel data without disturbing the trellis encoding, mapping, and Viterbi decoding of primary channel data, and without disturbing distribution preserving Tomlinson precoding and decoding of the primary channel data. In order to accommodate the secondary channel data, the secondary channel data are used to make quadrant decisions in a mapper, and concurrently therewith, dummy data or tertiary channel data corresponding in time with the secondary channel data are provided to the trellis encoder so that the continuous working of the trellis encoder can be maintained.

Abstract: A transmitter is provided with a distribution preserving Tomlinson coder which predistorts shaped data signals such that the power of each data signal exiting the coder is substantially similar to the power of the data signal entering the coder and such that upon transmission of the predistorted data signal over a channel, the effect of ISI of the channel is substantially removed. The transmitter is primarily intended for coded modulation systems utilizing a "coset" code, and the predistortion is preferably accomplished according to a linear function ##EQU1## where r.sub.k is a data signal entering the coder, a and.sub.i b.sub.i are the coefficients of polynomials relating to the channel impulse response, x.sub.k is the predistorted data signal exiting the coder, and s.sub.k is chosen to cause the signal power of x.sub.k on average to approximately equal the signal power of r.sub.k on average. Different methods for so choosing s.sub.k are disclosed.

Abstract: A transmitter is provided with a distribution preserving Tomlinson coder which predistorts shaped data signals such that the power of each data signal exiting the coder is substantially similar to the power of the data signal entering the coder and such that upon transmission of the predistorted data signal over a channel, the effect of ISI of the channel is substantially removed. The transmitter is primarily intended for coded modulation systems utilizing a "coset" code, and the predistortion is preferably accomplished according to a linear function ##EQU1## where r.sub.k is a data signal entering the coder, a.sub.l and b.sub.l are the coefficients of polynomials relating to the channel impulse response, x.sub.k is the predistorted data signal exiting the coder, and s.sub.k is a multiple of a given value (N) which is chosen to cause x.sub.k and r.sub.k to occupy identical defined regions in space, where the total length of each defined region is the given value N.

Abstract: An encoder is provided for generating rotationally invariant trellis codes when used with a signal constellation having m subconstellations indexed by j, each subconstellation having a plurality of points, where each subconstellation is a distinct rotation by j(360/m) degrees of another subconstellation such that no subconstellation has a point in common with another subconstellation. The encoder has a state block and a state update block. The state means receives q inputs i, and generates m outputs j, where m=pq and where p and q are integers greater than one and have no common factors. Outputs m are generated according to inputs i and states s of the state block according to j=i mod q and jd=s mod p, where the state block can assume n states, and n=md where d is an integer greater than one and has no common factors with p.

Abstract: A method is disclosed for determining with only sixty-four distance comparisions the distances between a received eight-dimensional vector comprised of four two-dimensional coordinates and each of sixteen non-overlapping subconstellations. In order to limit the comparisons, each subconstellation is represented by a collection of sixteen representational four-coordinate vectors, with each collection having four groups of vectors of the form______________________________________ (a, b, c, d) (a + 2, b + 2, c, d) (a, b, c + 2, d + 2) (a + 2, b + 2, c + 2, d + 2) ______________________________________where each letter represents in a different plane one of a set of points T(0) and its ninety, one hundred and eighty, and two hundred and seventy degree rotations, and +2 represents a one hundred and eighty degree rotation.