Information Theoretic Foundations of Adaptive Coded Modulation

In wireless/mobile communications, terminals adapt their rate and transmit power or, more in general, their coding and modulation scheme, depending on the time-varying channel conditions. This paper presents, in a tutorial form, the information theoretic framework underlying such ldquoadaptive modulationrdquo techniques. First, we review fading channel models, channel state information assumptions, and related capacity results. Then, we treat the case of input power constraint, where the optimal input distribution is Gaussian. Finally, we address the case of discrete modulations. In order to treat the latter, we make use of the recently developed method of ldquomercury-waterfillingrdquo, based on the relationship between mutual information and minimum mean-square error (MMSE) estimation of the channel input from the channel output. While the traditional design of adaptive modulation schemes based on uncoded bit-error rate (BER) involves the optimization over a discrete set of signal constellations, when powerful (i.e., capacity approaching) coding schemes are used the corresponding adaptive coded modulation design becomes surprisingly simple. The regime of very powerful coding is justified by the use of modern coding schemes, such as turbo codes and low-density parity-check codes, able to perform close to channel capacity at very small BER.