Optimized Irregular Low-Density Parity-Check Codes for Multicarrier Modulations over Frequency-Selective Channels
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Optimized Irregular Low-Density Parity-Check Codes for Multicarrier Modulations over Frequency-Selective Channels ´ Valerian Mannoni ETIS/ENSEA/UCP CNRS 8051, 6 Avenue du Ponceau 95014 Cergy-Pontoise Cedex, France Laboratory of Decision and Communications Systems (D´eCom), University of Reims Champagne-Ardenne, UFR Sciences, Moulin de la Housse, 51687 Reims Cedex 2, France Email: [email protected]
David Declercq ETIS/ENSEA/UCP CNRS 8051, 6 Avenue du Ponceau 95014 Cergy-Pontoise Cedex, France Email: [email protected]
Guillaume Gelle Laboratory of Decision and Communications Systems (D´eCom), University of Reims Champagne-Ardenne, UFR Sciences, Moulin de la Housse, 51687 Reims Cedex 2, France Email: [email protected] Received 1 March 2003; Revised 30 October 2003 This paper deals with optimized channel coding for OFDM transmissions (COFDM) over frequency-selective channels using irregular low-density parity-check (LDPC) codes. Firstly, we introduce a new characterization of the LDPC code irregularity called “irregularity profile.” Then, using this parameterization, we derive a new criterion based on the minimization of the transmission bit error probability to design an irregular LDPC code suited to the frequency selectivity of the channel. The optimization of this criterion is done using the Gaussian approximation technique. Simulations illustrate the good performance of our approach for different transmission channels. Keywords and phrases: orthogonal frequency division multiplexing, frequency-selective channel, optimized channel coding, irregular LDPC codes, density evolution.
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INTRODUCTION
In this paper, we address the problem of designing codes for transmissions over frequency-selective channels when orthogonal frequency division multiplexing (OFDM) modulation technique is used. Multicarrier modulations are good candidates for the emerging high rate transmissions, either wired, wireless, single, or multiuser. Several standards have chosen OFDM modulation because it allows a very simple mitigation of intersymbol interference (ISI), which could be very destructive when the information rate is high [1, 2]. The OFDM modulator transforms a frequency-selective channel into a set of flat-fading channels, which are easier to equalize. The problem of channel coding for OFDM systems (CodedOFDM or COFDM) has been already addressed [3]. Based on the emerging capacity approaching coding schemes, we propose an alternative coding structure for COFDM. In some
applications, like wired xDSL transmissions, there exists a backward channel that propagates some information from the receiver back to the transmitter. Properly used, this information can give to the transmitter an estimation of the channel that is going to be crossed. We propose in this paper to make use of this Information to design a code that is adapted to a frequency-selective OFDM channel. Although we assume perfect channel state information (CSI) at the transmitter, we will see that partial CSI is sufficient for our code design. In 1948,
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