Orthogonal Codes for Robust Low-Cost Communication

TL;DR

This paper explores the use of orthogonal coding schemes to achieve robust, low-cost communication over uncertain channels, extending capacity results to compound memoryless channels with a minimax approach.

Contribution

It introduces a minimax framework for orthogonal codes in compound channels, deriving achievable rates and demonstrating conditions for optimal capacity achievement.

Findings

Orthogonal codes can achieve the CPUC in compound channels under convex uncertainty.

A minimax formulation provides robustness against channel uncertainties.

Optimal performance is attained with mixed strategies combining different input symbols.

Abstract

Orthogonal coding schemes, known to asymptotically achieve the capacity per unit cost (CPUC) for single-user ergodic memoryless channels with a zero-cost input symbol, are investigated for single-user compound memoryless channels, which exhibit uncertainties in their input-output statistical relationships. A minimax formulation is adopted to attain robustness. First, a class of achievable rates per unit cost (ARPUC) is derived, and its utility is demonstrated through several representative case studies. Second, when the uncertainty set of channel transition statistics satisfies a convexity property, optimization is performed over the class of ARPUC through utilizing results of minimax robustness. The resulting CPUC lower bound indicates the ultimate performance of the orthogonal coding scheme, and coincides with the CPUC under certain restrictive conditions. Finally, still under the convexity property, it is shown that the CPUC can generally be achieved, through utilizing a so-called mixed strategy in which an orthogonal code contains an appropriate composition of different nonzero-cost input symbols.