Optimal integer bit-loading for multicarrier ADSL systems subject to spectral-compatibility limits

doi:10.1016/j.sigpro.2003.12.004

Signal Processing

Volume 84, Issue 4, April 2004, Pages 729-741

https://doi.org/10.1016/j.sigpro.2003.12.004 Get rights and content

Abstract

In this paper, we develop and test new algorithms for the optimal discrete bit-loading of digital subscriber loop (DSL) multicarrier (MC) systems when constraints on both the total available energy and the maximum energies per carrier are active. Although pressing spectral-compatibility issues limit performance of emerging G.DMT-based wide-band ADSL services, nevertheless, up to now none of the several published discrete-loading algorithms claiming optimality accounts for peak-energy limitations. Therefore, after proving the matroid structure of the underlying combinatorial optimization problem, we develop fast-implementable iterative greedy-type algorithms that converge to the desired optimal discrete loading. Several numerical results and comparisons carried out on standardized ADSL loops are presented that allow us to evaluate the system's losses induced by the imposed spectral-compatibility constraints.

Section snippets

System modeling, motivations and goals

DSL modems employ frequency bands above the traditional voice ones to convey high-speed data. Since in these utilized bands the telephone channels are severely frequency selective, an appealing approach to cope with the resulting inter-symbol interference (ISI) is to resort to multicarrier modulation (in particular, discrete multitone modulation) which divides the allowable band into several orthogonal (theoretically ISI-free) subchannels [4], [20].

The proposed optimal integer-bit loading algorithm

To apply Property 1 to the constrained combinatorial optimization problem of Section 1.1, we begin by noting that the assumed strictly increasing property of the rate-function $R (·)$ allows us to translate each constraint (9c) on ε_j^max into an equivalent constraint on the maximum number of bits b_j^max conveyable by jth subchannel, according to the (quite obvious) relationship $b_{j}^{max} =⌊ R (ρ_{j} ε_{j}^{max})⌋, j=1,…,N_{c},$ where ⌊·⌋ denotes the floor function. Therefore, on the basis of (13) the original constrained

Some application-oriented comments about the proposed bit-loading algorithm

According to the greedy approach, at each step the algorithm of Table 2 adds a bit to the subchannel requiring the smallest incremental energy and which has not already reached its maximum b_j^max. At the end of each step, dummy variables ε_sum and B_tot store the overall energy and the number of bits currently allocated by the algorithm. This last stops when ε_sum exceeds ε_tot or when each subchannel conveys the maximum allowed number of bits b_j^max. Eventually, after execution of the algorithm, the

Numerical tests and performance comparisons

To evaluate the throughput loss induced by peak-energy constraints imposed by emerging spectral compatibility issues [13], we have tested the performance of the proposed algorithm of Table 2 on some ANSI channels, namely the so-called T1.9, CSA4, CSA6 and mid-CSA6 loops (see, for example, [7], [20] for a detailed description of these links). The simulated transmission system is the G.DMT one planned by ANSI for emerging high-throughput ADSL-based multimedia services, whose key-parameters are

Conclusions

In this contribution we have solved CRAL and CMAL problems arising in emerging G.DMT-based ADSL systems when hard spectral-compatibility limitations on the allowable peak-energies must be met [2], [19]. We have proved that the considered combinatorial optimization problems exhibit a matroid structure so that greedy approaches are optimal for solving them. Thus, new greedy-type low-complexity algorithms converging to the optimal integer-bit distributions have been developed and their

References (22)

C. Assimakopoulos, F.-N. Pavlidou, Comparative study of loading algorithms for PLC applications, ISPLC2002 Proceedings,...
Asymmetric digital subscriber line (ADSL) metallic interface, ANSI Std....
E. Baccarelli et al.
Novel efficient bit-loading algorithms for peak-energy-limited ADSL-type multicarrier systems
IEEE Trans. Signal Process.
(May 2002)
J.A.C. Bingham
ADSL, VDSL and Multicarrier Modulation
(2002)
J. Campello, Practical bit loading for DMT, IEEE ICC’99 Proceedings, June 1999, Vancouver, pp....
P.S. Chow et al.
A practical discrete multitone transceiver loading algorithm for data transmission over spectrally shaped channels
IEEE Trans. Comm.
(February/March/April 1995)
J.M. Cioffi et al.
MMSE decision-feedback equalizers and coding, II. Coding results
IEEE Trans. Comm.
(October 1995)
J. Edmonds
Matroids and greedy algorithms
Math. Programming
(1971)
A. Federgruen et al.
The greedy procedure for resource allocation problemsnecessary and sufficient conditions for optimality
Oper. Res.
(1986)
R.F.H. Fisher, J.B. Huber, A new loading algorithm for discrete multitone transmission, IEEE Globecom’96 Proceedings,...

S. Galli, T.C. Banwell, A novel approach to the accurate modeling of the indoor power line channel, Part II—Transfer...

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Optimal integer bit-loading for multicarrier ADSL systems subject to spectral-compatibility limits

Abstract

Section snippets

System modeling, motivations and goals

The proposed optimal integer-bit loading algorithm

Some application-oriented comments about the proposed bit-loading algorithm

Numerical tests and performance comparisons

Conclusions

Novel efficient bit-loading algorithms for peak-energy-limited ADSL-type multicarrier systems

IEEE Trans. Signal Process.

ADSL, VDSL and Multicarrier Modulation

A practical discrete multitone transceiver loading algorithm for data transmission over spectrally shaped channels

IEEE Trans. Comm.

MMSE decision-feedback equalizers and coding, II. Coding results

IEEE Trans. Comm.

Matroids and greedy algorithms

Math. Programming

The greedy procedure for resource allocation problemsnecessary and sufficient conditions for optimality

Oper. Res.