Skip to Main Content
In broadcast scenarios or in the absence of accurate channel probability distribution information, code design for consistent channel-by-channel performance, rather than average performance over a channel distribution, may be desirable. Root and Varaiya's compound channel theorem for linear Gaussian channels promises the existence of universal codes that operate reliably whenever the channel mutual information (MI) is above the transmitted rate. This paper presents 2-D trellis codes that provide such universal performance over the compound linear vector Gaussian channel when demultiplexed over two, three, and four transmit antennas. The presented trellis codes are found by an exhaustive search that guarantees consistent performance on every matrix channel that supports the information transmission rate with an MI gap that is similar to the capacity gap of a well-designed additive white Gaussian noise (AWGN)-specific code on the AWGN channel. As a result of their channel-by-channel consistency, the universal trellis codes presented here also deliver comparable, or in some cases, superior frame-error rate and bit-error rate performance under quasi-static Rayleigh fading to trellis codes of similar complexity that are designed specifically for the quasi-static Rayleigh fading scenario.