LDPC Code Design for Nonuniform Power-Line Channels
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Research Article LDPC Code Design for Nonuniform Power-Line Channels Ali Sanaei and Masoud Ardakani Department of Electrical and Computer Engineering, Faculty of Engineering, University of Alberta, Edmonton, AB, Canada T6G 2V4 Received 28 October 2006; Revised 8 March 2007; Accepted 1 May 2007 Recommended by Lutz Lampe We investigate low-density parity-check code design for discrete multitone channels over power lines. Discrete multitone channels are well modeled as nonuniform channels, that is, different bits experience various channel parameters. We propose a coding system for discrete multitone channels that allows for using a single code over a nonuniform channel. The number of code parameters for the proposed system is much greater than the number of code parameters in conventional channel. Therefore, search-based optimization methods are impractical. We first formulate the problem of optimizing the rate of an irregular low-density parity-check code, with guaranteed convergence over a general nonuniform channel, as an iterative linear programming which is significantly more efficient than search-based methods. Then we use this technique for a typical power-line channel. The methodology of this paper is directly applicable to all decoding algorithms for which a density evolution analysis is possible. Copyright © 2007 A. Sanaei and M. Ardakani. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
1.
INTRODUCTION
Discrete multitone (DMT) modulation is widely used in power-line communications. DMT modulation is almost always used in conjunction with channel coding, which is called coded DMT. In the past few years, some of the modern coding techniques such as low-density parity-check (LDPC) coding and turbo coding are proposed for coded DMT systems [1–5]. The motivation for using these codes has been their phenomenal performance with practical complexity. In previous works on applying turbo and LDPC codes to power-line and general DMT channels, the channel is usually assumed to be uniform over all frequency tones. In practice, however, the channel SNR varies from one frequency tone to another. That is to say, if all the frequency tones are assigned to a single binary code, different bits of the codeword are received with different qualities at the receiver. This can seriously harm the iterative decoding process. The method proposed in [5] mitigates the effects of nonuniformity in the DMT channels by using QAM constellations of possibly different sizes in different frequency tones. The size of the QAM constellation is selected according to the SNR of the tone. Then a certain number of least significant bits from each QAM constellation (2 bits in this case) are Gray labeled and all higher bits are Ungerboeck labeled. The Gray-labeled bits are then assigned to a binary LDPC code. The Ungerboeck-labeled bits are coded separately with
other codes (hence they do not
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