Stefan Höst

The fourth generation broadband concept

Fixed-broadband access technology is evolving from exclusively copper-based solutions to hybrid fiber-copper architectures. This article presents the expected next step in the evolution of broadband systems, which we call the fourth-generation broadband concept. It identifies a technical, infrastructural, and economical niche and describes how the fiber-access network is extended and forked to feed a last and ultimate generation of DSL systems, shown to have gigabit potential. The underlying infrastructural concept is presented, economic aspects are described and discussed, and achievable data rates are calculated.

Active distances for convolutional codes

A family of active distance measures for general convolutional codes is defined. These distances are generalizations of the extended distances introduced by Thommesen and Justesen (1983) for unit memory convolutional codes. It is shown that the error correcting capability of a convolutional code is determined by the active distances. The ensemble of periodically time-varying convolutional codes is defined and lower bounds on the active distances are derived for this ensemble. The active distances are very useful in the analysis of concatenated convolutional encoders.

Woven convolutional codes .I. Encoder properties

Encoders for convolutional codes with large free distances can be constructed by combining several less powerful convolutional encoders. This paper is devoted to constructions in which the constituent convolutional codes are woven together in a manner that resembles the structure of a fabric. The general construction is called twill and it is described together with two special cases, viz., woven convolutional encoders with outer warp and with inner warp. The woven convolutional encoders inherit many of their structural properties, such as minimality and catastrophicity, from their constituent encoders. For all three types of woven convolutional codes upper and lower bounds on their free distances as well as lower bounds on the active distances of their encoders are derived.

Woven convolutional codes. II: decoding aspects

An iterative decoding scheme for woven convolutional codes is presented. It operates in a window sliding over the received sequence. This exploits the nature of convolutional codewords as infinite sequences and reflects the concept of considering convolutional encoding and decoding as a continuous process. The decoder is analyzed in terms of decoding delay and decoding complexity. Its basic building block is a symbol-by-symbol a posteriori probability (APP) decoder for convolutional codes, which is a windowed variant of the well-known Bahl-Cocke-Jelinek-Raviv (BCJR) algorithm. Additional interleaving for the woven constructions is introduced by employing convolutional scramblers. It is shown that row-wise random interleaving preserves the lower bound on the free distance of the original woven constructions. Based on the properties of the interleavers, new lower bounds on the free distance of woven constructions with both outer warp and inner warp are derived. Simulation results for woven convolutional codes with and without additional interleaving are presented.

Optimizing Power Normalization for G.fast Linear Precoder by Linear Programming

The use of vectoring for crosstalk cancellation in the new ITU-T G.fast standard for next generation DSL systems becomes essential for efficient utilization of the extended bandwidth (up to 200 MHz). In VDSL2 (up to 30 MHz), a zero-forcing-based linear precoder is used in downstream which approaches single-line performance. However, at high frequencies, the linear precoder may amplify the signal power substantially since the crosstalk channel is much stronger than at lower frequencies. Performance could be significantly degraded by power normalization to keep the PSD below the mask. In this work, we extended a per-line power normalization scheme by linear programming (LP) optimization. By simulations using measured cable data it is shown how the LP-based scheme further improves the linear precoder and it is also capable of balancing the data rate between lines. Further, the simulations also show the non-linear Tomlinson-Harashima precoder performs better than the linear precoders.

Simple and Causal Copper Cable Model Suitable for G.fast Frequencies

G.fast is a new standard from the International Telecommunication Union, which targets 1 Gb/s over short copper loops using frequencies up to 212 MHz. This new technology requires accurate parametric cable models for simulation, design, and performance evaluation tests. Some existing copper cable models were designed for the very high speed digital subscriber line spectra, i.e., frequencies up to 30 MHz, and adopt assumptions that are violated when the frequency range is extended to G.fast frequencies. This paper introduces a simple and causal cable model that is able to accurately characterize copper loops composed by single or multiple segments, in both frequency and time domains. Results using G.fast topologies show that, apart from being accurate, the new model is attractive due to its low computational cost and closed-form expressions for fitting its parameters to measurement data.

Low‐Order and Causal Twisted‐Pair Cable Modeling by Means of the Hilbert Transform

A new low-order and causal twisted-pair cable model for the copper access network is derived. From the serial resistance of the widely used, but non-causal, BT0 model, the serial inductance is computed via the Hilbert transform. By doing so, a causal cable model is obtained containing fewer parameters compared to the BT0 model. The deviation between the two models is evaluated for the standardized ETSI cables.

On the error exponent for woven convolutional codes with outer warp

In this correspondence, the error exponents and decoding complexity of binary woven convolutional codes with outer and inner warp are studied. It is shown that for both constructions an error probability that is exponentially decreasing with the memory of the woven convolutional codes can be achieved with a nonexponentially increasing decoding complexity. Furthermore, the error exponent for woven convolutional codes with inner warp is larger than the one for woven convolutional codes with outer warp.

Woven convolutional codes and unequal error protection

Woven convolutional codes with outer warp are used to construct a generator matrix with an effective free distance vector that is lower bounded by the free distances of the component codes. This enables the construction of convolutional codes with unequal error protection.

Simple and causal twisted-pair channel models for G.fast Systems

The use of a hybrid copper and fiber architecture is attractive in both fixed access and mobile backhauling scenarios. This trend led the industry and academia to start developing the fourth generation broadband system, which aims at achieving bit-rates of 1 Gb/s over short copper loops. In this context, accurate models of short twisted-pair cables operating at relatively high frequencies are key elements. This work describes new parametric cable models that incorporate four important characteristics: support of frequencies up to 200 MHz, few parameters, causal impulse responses and require relatively easy fitting procedures. The results show that the models achieve good accuracy for single segments, which are the expected topology for G.fast deployments.