Near-Capacity Coding for Discrete Multitone Systems with Impulse Noise
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Near-Capacity Coding for Discrete Multitone Systems with Impulse Noise Masoud Ardakani,1 Frank R. Kschischang,2 and Wei Yu2 1 Department
of Electrical and Computer Engineering, University of Alberta, ECERF Building, Edmonton, AB, Canada, T6G 2V4 of Electrica and Computer Engineering, University of Toronto, 10 King’s College Road, Toronto, ON, Canada M5S 3G4
2 Department
Received 1 December 2004; Revised 28 April 2005; Accepted 9 June 2005 We consider the design of near-capacity-achieving error-correcting codes for a discrete multitone (DMT) system in the presence of both additive white Gaussian noise and impulse noise. Impulse noise is one of the main channel impairments for digital subscriber lines (DSL). One way to combat impulse noise is to detect the presence of the impulses and to declare an erasure when an impulse occurs. In this paper, we propose a coding system based on low-density parity-check (LDPC) codes and bit-interleaved coded modulation that is capable of taking advantage of the knowledge of erasures. We show that by carefully choosing the degree distribution of an irregular LDPC code, both the additive noise and the erasures can be handled by a single code, thus eliminating the need for an outer code. Such a system can perform close to the capacity of the channel and for the same redundancy is significantly more immune to the impulse noise than existing methods based on an outer Reed-Solomon (RS) code. The proposed method has a lower implementation complexity than the concatenated coding approach. Copyright © 2006 Hindawi Publishing Corporation. All rights reserved.
1.
INTRODUCTION
The design of error control codes for discrete multitone (DMT) systems is of great interest for applications such as digital subscriber lines (DSL) [1–6]. In a DMT system, different constellations may be used in different tones and nonbinary high-order modulation formats are typically used. Current asymmetric DSL (ADSL) standards use a trelliscoded modulation scheme concatenated with an outer ReedSolomon (RS) code. The inner trellis code provides a coding gain for an additive white Gaussian noise (AWGN) channel, and the outer RS code offers additional noise immunity, especially against impulse noise. This paper is motivated by the phenomenal success of turbo and low-density parity-check (LDPC) codes in the past decade. It is now possible to design codes that perform within a fraction of a decibel (dB) from the Shannon limit in an additive white Gaussian noise channel. However, the use of turbo codes and LDPC codes in DMT systems is not yet widespread. This is in part due to the fact that the effect of impulse noise on turbo or LDPC codes has not yet been studied in depth. Impulse noise is one of the main channel impairments in DSL. The main focus of this paper is the design of LDPC codes for a DMT system in an impulse-noise environment.
In their original forms, both turbo and LDPC codes are binary codes. In the low signal-to-noise-ratio (SNR) regime, where binary modulation is spectrally efficient, binary turbo codes and
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