Johannes B. Huber

Multilevel codes: theoretical concepts and practical design rules

This paper deals with 2/sup l/-ary transmission using multilevel coding (MLC) and multistage decoding (MSD). The known result that MLC and MSD suffice to approach capacity if the rates at each level are appropriately chosen is reviewed. Using multiuser information theory, it is shown that there is a large space of rate combinations such that MLC and full maximum-likelihood decoding (MLD) can approach capacity. It is noted that multilevel codes designed according to the traditional balanced distance rule tend to fall in the latter category and, therefore, require the huge complexity of MLD. The capacity rule, the balanced distances rules, and two other rules based on the random coding exponent and cutoff rate are compared and contrasted for practical design. Simulation results using multilevel binary turbo codes show that capacity can in fact be closely approached at high bandwidth efficiencies. Moreover, topics relevant in practical applications such as signal set labeling, dimensionality of the constituent constellation, and hard-decision decoding are emphasized. Bit interleaved coded modulation, proposed by Caire et al. (see ibid., vol.44, p.927-46, 1998), is reviewed in the context of MLC. Finally, the combination of signal shaping and coding is discussed. Significant shaping gains are achievable in practice only if these design rules are taken into account.

A new loading algorithm for discrete multitone transmission

A new loading algorithm for discrete multitone transmission is proposed. Thereby rate is not distributed according to channel capacity, but rate and transmit power are assigned to maximize the signal-to-noise ratio in each carrier. Because closed form expressions can be derived the algorithm is of very low complexity, even lower than the loading algorithm recently proposed by Chow et al. (see IEEE Transactions on Communications, no.2/3/4, p.773-5, 1995). Nevertheless achievable performance is higher or at least the same. Results for a typical high rate transmission over twisted pair lines are presented.

Precoding in multiantenna and multiuser communications

In this paper, Tomlinson-Harashima Precoding for multiple-input/multiple-output systems including multiple-antenna and multiuser systems is studied. It is shown that nonlinear preequalization offers significant advantages over linear preequalization which increases average transmit power. Moreover, it outperforms decision-feedback equalization at the receiver side which is applicable if joint processing at the receiver side is possible, and which suffers from error propagation. A number of aspects of practical importance are studied. Loading, i.e., the optimum distribution of transmit power and rate is discussed in detail. It is shown that the capacity of the underlying MIMO channel can be utilized asymptotically by means of nonlinear precoding.

A comparison of peak power reduction schemes for OFDM

Two powerful and distortionless peak power reduction schemes for orthogonal frequency division multiplexing (OFDM) are compared. One investigated technique is selected mapping (SLM) where the actual transmit signal is selected from a set of signals and the second scheme utilizes phase rotated partial transmit sequences (PTS) to construct the transmit signal. Both approaches are very flexible as they do not impose any restriction on the modulation applied in the subcarriers or on their number. They both introduce some additional system complexity but nearly vanishing redundancy to achieve markedly improved statistics of the multicarrier transmit signal. The schemes are compared by simulation results with respect to the required system complexity and transmit signal redundancy.

A novel peak power reduction scheme for OFDM

An efficient and distortionless scheme for peak power reduction in orthogonal frequency division multiplexing (OFDM) is proposed, which introduces some additional complexity but nearly vanishing redundancy. The approach is very flexible and works with arbitrary numbers of subcarriers and without restriction on the type of modulation applied in them. The core of the approach is the coordination of appropriately phase rotated signal parts to minimize the peak power of the multiplex signal. The improved statistics of peak power in the optimized transmit signal are demonstrated by simulation results. Finally, it is shown that this scheme is close to the theoretical limit curve of redundancy versus minimum peak-to-average power ratio (PAR).

Lattice-reduction-aided broadcast precoding

A precoding scheme for multiuser broadcast communications is described, which fills the gap between the low-complexity Tomlinson-Harashima precoding and the sphere decoder-based system of Peel et al. Simulation results show that, replacing the closest-point search with the Babai approximation, the full diversity order supported by the channel is available to each user, as in the system of Peel et al., and unlike Tomlinson-Harashima precoding, which suffers some diversity penalty. The complexity of the scheme is similar to that of Tomlinson-Harashima precoding.

MIMO precoding for decentralized receivers

This paper presents a modified version of Tomlinson-Harashima type precoding applicable to a setting with decentralized receivers, e.g. in a DS-CDMA downlink scenario. Precoding, i.e., nonlinear pre-equalization, is an interesting strategy for significantly simplifying signal processing at the receiver side (mobile terminals) at only moderate additional complexity at the base station.

Power and bandwidth efficient digital communication using turbo codes in multilevel codes

The recently proposed Turbo codes are applied to bandwidth efficient modulation schemes via multilevel coding. For this purpose, Turbo codes are extended for a wide range of fine tunable rates by puncturing. A straightforward derivation of iterative Turbo decoding and the concept of extrinsic information is presented. New design rules for multilevel codes with arbitrary component codes and codeword lengths are derived from information theory. Simulation results show that application of Turbo codes to properly designed multilevel coding schemes leads to digital transmission schemes with high power and bandwidth efficiency.

An alternative approach to reduced-complexity CPM-receivers

By separating the two complexity problems connected with optimum coherent CPM (continuous phase modulation) receivers, namely, the number of linear filters and the number of memory states required, a straightforward procedure for reducing the complexity is proposed and its usefulness is evaluated. A concise analysis of the inherent trellis encoder associated with CPM is given. It is then demonstrated that for almost all schemes of interest in practice, it is quite sufficient for the receiver to implement only four or six linear filters which represent proper reference signals. For a reduction in the number of memory states, decision-feedback sequence estimation together with minimization of the unprocessed intersymbol interference is proposed. Modifications of this procedure allow a state reduction without losses or with only negligible losses because only error events with large distances are affected. Combinations of these methods make possible an almost continuous tradeoff between receiver complexity and SNR (signal/noise ratio) losses. Several examples are considered for which evaluations of minimum Euclidean distances and simulation results are given. >

Bounds on information combining

When the same data sequence is transmitted over two independent channels, or when a data sequence is transmitted twice but independently over the same channel, the independent observations can be combined at the receiver side. From an information-theory point of view, the overall mutual information between the data sequence and the received sequences represents a combination of the mutual information of the two channels. This concept is termed information combining. A lower bound and an upper bound on the combined information is presented, and it is proved that these bounds are tight. Furthermore, this principle is extended to the computation of extrinsic information on single code bits for a repetition code and for a single parity-check code of length three, respectively. For illustration of the concept and the bounds on information combining, two applications are considered. First, bounds on the information processing characteristic (IPC) of a parallel concatenated code are derived from its extrinsic information transfer (EXIT) chart. Second, bounds on the EXIT chart for an outer repetition code and for an outer single parity-check code of a serially concatenated coding scheme are computed.