Error Control of Line Codes Generated by Finite Coxeter Groups

A theory leading to the design of line group codes generated by Coxeter matrix groups was presented in [1]. With these codes, resistance to common-mode noise is obtained by using codewords whose components sum to zero, simultaneous switching output noise is reduced by using constant-energy signals, and the effects of intersymbol interference are reduced by having decisions based on only two values at the input of the final slicers. Codebook design is based on the theory of Group Codes for the Gaussian Channel [12], as specialized to Coxeter matrix groups generated by reflections in orthogonal hyperplanes. In this paper we discuss the introduction of error control coding in a way consistent with the constraints imposed on that design.