This paper presents an analytical study of a high-resolution positron ring detector system for transaxial reconstruction tomography. Our goal is a combination of good spatial resolution, high sensitivity, rejection of scattered photons, variable section thickness, and the minimization of the number of photomultipliers and coincidence circuits. A circular ring of 288 NaI(Tl) crystals 0.8 cm wide should provide a resolution of 4--7 mm FWHM over a circular region 30 cm in diameter. Coded light pipes permit readout using only 72 photomultipliers and 12 coincidence circuits. With properly designed shielding and an energy resolution of 30% FWHM, a positron activity of 200 muCi per axial centimeter in a 20-cm-diam cylinder of tissue should provide approximately 7,000 events/sex from a 2-cm-thick transaxial section (including a 5% accidental coincident background and a 26% scattered coincident background). This rate is adequate for both static and dynamic imaging. The device can operate at two to three times higher event rates with increased backgrounds.