Karl Marx, one of the founders of Communist philosophy, wrote:
Of course, in the beginning, this cannot be effected except by means of despotic inroads on the rights of property, and on the conditions of bourgeois production; by means of measures, therefore, which appear economically insufficient and untenable, but which, in the course of the movement, outstrip themselves, necessitate further inroads upon the old social order, and are unavoidable as a means of entirely revolutionising the mode of production.These measures will of course be different in different countries.Nevertheless in the most advanced countries, the following will be pretty generally applicable.1. Abolition of property in land and application of all rents of land to public purposes.2. A heavy progressive or graduated income tax.3. Abolition of all right of inheritance.4. Confiscation of the property of all emigrants and rebels.5. Centralisation of credit in the hands of the State, by means of a national bank with State capital and an exclusive monopoly.6. Centralisation of the means of communication and transport in the hands of the State.7. Extension of factories and instruments of production owned by the State; the bringing into cultivation of waste-lands, and the improvement of the soil generally in accordance with a common plan.8. Equal liability of all to labour. Establishment of industrial armies, especially for agriculture.9. Combination of agriculture with manufacturing industries; gradual abolition of the distinction between town and country, by a more equable distribution of the population over the country.10. Free education for all children in public schools. Abolition of children's factory labour in its present form. Combination of education with industrial production.
These are the means by which Marx proposed to bring Communism to the poor deluded masses. Note number 2 - A heavy progressive or graduated income tax.
If a progressive income tax is a requirement for Communism, then it's definitely tied closely to Socialism, which is, in effect, Communism Lite.
In other words, Carson was wrong, but only because he didn't go far enough.