Two-channel RSNS dynamic range

Symmetrical number systems have been explored for many applications in both analog and digital signal processing due to the common availability of symmetrical folding waveforms (e.g., cos² ). The robust symmetrical number system (RSNS) is a modular scheme in which the integer values within each modulus, when considered together, change one at a time at the next code position (Gray code properties). Although the RSNS has a smaller dynamic range than the optimum symmetrical number system, the RSNS Gray code properties make it particularly attractive for error control. In the past, computer search algorithms have been used to determine the RSNS dynamic range (length of unambiguous vectors). In this brief, we define the two-channel RSKS and present a theorem that gives its dynamic range for relatively prime moduli m₁, m₂, 5 ⩽ m₁ ⩽ m₂