We apply coset codes to adaptive modulation in fading channels. Adaptive modulation is a powerful technique to improve the energy efficiency and increase the data rate over a fading channel. Coset codes are a natural choice to use with adaptive modulation since the channel coding and modulation designs are separable. Therefore, trellis and lattice codes designed for additive white Gaussian noise (AWGN) channels can be superimposed on adaptive modulation for fading channels, with the same approximate coding gains. We first describe the methodology for combining coset codes with a general class of adaptive modulation techniques. We then apply this methodology to a spectrally efficient adaptive M-ary quadrature amplitude modulation (MQAM) to obtain trellis-coded adaptive MQAM. We present analytical and simulation results for this design which show an effective coding gain of 3 dB relative to uncoded adaptive MQAM for a simple four-state trellis code, and an effective 3.6-dB coding gain for an eight-state trellis code. More complex trellis codes are shown to achieve higher gains. We also compare the performance of trellis-coded adaptive MQAM to that of coded modulation with built-in time diversity and fixed-rate modulation. The adaptive method exhibits a power savings of up to 20 dB.

We introduce a general adaptive coding scheme for Nakagami multipath fading channels. An instance of the coding scheme utilizes a set of 2 -dimensional (2 -D) trellis codes originally designed for additive white Gaussian noise (AWGN) channels. Any set of 2 -D trellis codes for AWGN channels can be used. Sets for which all codes can be generated by the same encoder and decoded by the same decoder are of particular interest. A feedback channel between the transmitter and receiver makes it possible to transmit at high spectral efficiencies under favorable channel conditions and respond to channel degradation through a smooth reduction of the spectral efficiency. We develop a general technique to determine the average spectral efficiency of the coding scheme for any set of 2 -D trellis codes. As an illustrative example, we calculate the average spectral efficiency of an adaptive codec utilizing eight 4-D trellis codes. The example codec is based on the International Telecommunications Union's ITU-T V.34 modem standard.

The well-known uniform error property for signal constellations and codes is extended to encompass information bits. We introduce a class of binary labelings for signal constellations, called bit geometrically uniform (BGU) labelings, for which the uniform bit error property holds, i.e., the bit error probability does not depend on the transmitted signal. Strong connections between the symmetries of constellations and binary Hamming spaces are involved. For block-coded modulation (BCM) and trellis-coded modulation (TCM) Euclidean-space codes, BGU encoders are introduced and studied. The properties of BGU encoders prove quite useful for the analysis and design of codes aimed at minimizing the bit, rather than symbol, error probability. Applications to the analysis and the design of serially concatenated trellis codes are presented, together with a case study which realizes a spectral efficiency of 2 b/s/Hz.

[18] R. R. Müller, “On the asymptotic eigenvalue distribution of concatenated