For channels with severe amplitude distortion such as high-speed digital subscriber loops, using a Tomlinson-Harashima (TH) precoder in the transmitter has the same intersymbol-interference-elimination and noise-suppression advantages as using a decision feedback equalizer in the receiver, but without its disadvantage of error propagation. TH precoders have a further advantage of interworking easily with coded modulation techniques. Square constellations are generally preferred in systems using conventional TH precoders. The choice for the size of square constellations is, however, limited. The authors widen that choice by designing new families of generalized square and hexagonal constellations together with their matched generalized TH precoders. The design of the constellation and TH precoder is closely related to the design. Using a generalized TH precoder also results in a smaller peak-to-average power ratio of the transmitted signal than that for conventional TH precoders. Simple modifications of Viterbi decoders required by the use of TH precoders are also discussed.>

A number of two-level codes based on trellis-coded modulation (TCM) schemes and their matched single or double error-correcting Reed-Solomon codes using QAM constellations are presented and evaluated. Compared to the well-known 4D 16-state TCM scheme with a comparable bandwidth efficiency, these two-level codes provide greater immunity from both Gaussian and impulse noise, at the cost of a reasonably higher complexity and a longer decoding delay, on the order of a few hundred symbols. The authors also show how to cope with phase ambiguities of the constellation in these two-level codes. Both rotationally invariant coding and rotation detecting techniques are considered.>

An equivalent partial-response (PR) channel 1-Z/sup -k/ arises in the envisioned terrestrial over-the-air broadcasting of digital high-definition television (HDTV) signals when a comb filter is used by an HDTV receiver to reduce the NTSC cochannel interference. The design of signal constellations and their associated precoders for this PR channel is considered. Besides PAM and square QAM, it is shown that generalized square and hexagonal constellations can also be used. Coded modulation and graceful degradation in the received signal quality are discussed. The results extended to a more general PR channel.>

It is always desirable to maintain communications in difficult situations, even though fewer messages can get across. The author has developed such capabilities for one-way broadcast media, such as the envisioned terrestrial broadcasting of digital high-definition television signals. In this television broadcasting, the data from video source encoders are not equally important. It is desirable that the important data be recovered by each receiver even under poor receiving conditions. Two approaches for providing such unequal error protection to different classes of data are presented. Power-efficient and bandwidth-efficient coded modulation is used in both approaches. The first approach is based on novel signal constellations with nonuniformly spaced signal points. The second uses time division multiplexing of different conventional coded modulation schemes. Both approaches can provide error protection for the important data to an extent that can hardly be achieved using conventional coded modulation with equal error protection. For modest amounts of important data, the first approach has, additionally, the potential of providing immunity from impulse noise through simple bit or signal-point interleaving.>

Good coded modulation for fading channels requires built-in time diversity. Under a constraint on the interleaving delay, the authors construct and compare three categories of coded M-DPSK (M-ary differential phase-shift keying) schemes with 4>

The authors discuss the major attributes desired in signal constellations, such as signal-to-noise ratio (SNR) efficiency, simplicity of mapping bits to points and vice versa, compatibility with coded modulation schemes, and compatibility with quadrature amplitude modulation (QAM). The capability of supporting a so-called opportunistic secondary channel, often used for internal control signaling, is considered. The gain in SNR efficiency of a multidimensional constellation (lattice code) consisting of the points from a lattice Lambda within a region R compared to a cubic constellation is shown to be approximately separable into the coding gain of Lambda and the shape gain of R, for large constellations. Similarly, the expansion of the associated constituent 2-D constellation is shown to be approximately separable into a constellation expansion ratio (CER) coding component CER/sub c/( Lambda ) and a shaping component CER/sub s/(R). The N sphere is the region R with the best shape gain, but N also has large constellation expansion. Bounds for the best possible shape gain versus CER/sub s/(R) or peak-to-average-power ratio (PAR) are given. Generalized cross constellations are discussed. These constellations yield a modest shape gain with very low CER/sub s/(R) or PAR, are easily implemented, are well suited for use with coded QAM modems, and can be readily adapted to support an opportunistic secondary channel.>

Using a multidimensional approach, the author discovers a large family of rotationally invariant trellis-coded M-PSK (M-ary shift keying) schemes, M>or=8, with nominal coding gains ranging from 3 to 5 dB and with bandwidth requirements the same as, or even less than, those of uncoded M/2-PSK schemes at the same information bit rate. The rotationally invariant schemes have performance and complexities comparable to the best known nonrotationally-invariant trellis-coded two-dimensional M-PSK schemes. Computer simulation results for these schemes, assuming an additive white-Gaussian-noise (AWGN) channel, are reported.>

Trellis-coded modulation schemes using four-, eight-, or16-dimensional constellations have a number of potential advantages over the usual two-dimensional schemes: a smaller constituent two-dimensional constellation, easier tolerance to phase ambiguities, and a better trade-off between complexity and coding gain. A number of such schemes are presented and evaluated. Starting with a variety of multidimensional lattices, we show how to select multidimensional constellations, how to partition them into subsets, how to construct trellis codes using those subsets, and how to map hits to constellation points. Simplifications of the Viterbi decoding algorithm are presented. We conclude that there are multidimensional trellis-coded modulation schemes that perform better for the same complexity than do two-dimensional schemes.

Convolutional channel coding with expanded signal space improves error performance of synchronous data links without sacrificing data rate or requiring more bandwidth. Due to the phase ambiguity(ies) in the expanded signal space, it is desirable to design the code' to be transparent to signal element rotations. In this paper, design rules and procedures for 180° rotationally invariant codes are presented. In a companion paper, we extend these rules and procedures to codes which are transparent to 90, 180, and 270° signal element rotations. We illustrate these rules and procedures by designing simple codes that achieve coding gain of 3-4 dB. These are the codes of practical interest. Codes with higher coding gain can be obtained using the same rules and procedures. Both feedforward and feedback codes are considered.

This is the second paper on rotationally invariant convolutional channel coding with expanded signal space. Signal space with 90, 180, and 270° phase ambiguities is generally preferred to signal space with only 180° phase ambiguity. In this paper, design rules and procedures for 180° rotationally invariant convolutional codes in the previous paper are extended to rotationally invariant codes with expanded signal space having 90, 180, and 270° phase ambiguities. As in the previous paper, we illustrate these rules and procedures by designing simple codes with coding gain of 4 dB. Nonlinear convolutional codes result from these design rules and procedures. These simple nonlinear convolutional codes are being considered as international standards on voiceband modems at rate greater than or equal to 9.6 kbits/s. Codes with higher coding gain can be obtained using the same rules and procedures. Both feedforward and feedback codes are considered. In addition, a new class of codes described as "generalized feedback" is also considered.