CONVOLUTIONAL ENCODERS FOR MODEMS WHICH IMPLEMENT THE "COLE CODE"

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.1 are taken as outputs and are also used on conjunction with the convolutional encoder to generate a fifth output y.sub.0. With state variables x(n-1), p(n-1), r(n-1), r(n-2), s(n-1), s(n-2) relabled as w.sub.1, w.sub.2, w.sub.3, w.sub.4, w.sub.5, and w.sub.6, output y.sub.0 is taken as state variable w.sub.5. The state variables are updated according to: new w.sub.6 =w.sub.5 ; new w.sub.5 =y.sub.2 +w.sub.3 +w.sub.6 ; new w.sub.4 =w.sub.3 ; new w.sub.3 =y.sub.1 +w.sub.3 w.sub.4 +w.sub.2 +w.sub.1 ; new w.sub.2 =y.sub.3 +(new w.sub.3)w.sub.3 +w.sub.4 +w.sub.3 (new w.sub.5)+w.sub.3 w.sub.6 ; and new w.sub.1 =y.sub.4 +w.sub.2. In the three-to-four systematic Cole code, y.sub.4 is taken as zero.