Article

# Design of Low-Density Parity-Check Codes for Modulation and Detection

Bell Labs., Crawford, NJ, USA
(Impact Factor: 1.99). 05/2004; 52(4):670 - 678. DOI: 10.1109/TCOMM.2004.826370
Source: IEEE Xplore

ABSTRACT

A coding and modulation technique is studied where the coded bits of an irregular low-density parity-check (LDPC) code are passed directly to a modulator. At the receiver, the variable nodes of the LDPC decoder graph are connected to detector nodes, and iterative decoding is accomplished by viewing the variable and detector nodes as one decoder. The code is optimized by performing a curve fitting on extrinsic information transfer charts. Design examples are given for additive white Gaussian noise channels, as well as multiple-input, multiple-output (MIMO) fading channels where the receiver, but not the transmitter, knows the channel. For the MIMO channels, the technique operates within 1.25 dB of capacity for various antenna configurations, and thereby outperforms a scheme employing a parallel concatenated (turbo) code by wide margins when there are more transmit than receive antennas.

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Available from: Alexei Ashikhmin, Dec 05, 2014
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• "An equivalent model called herein the " virtual " channel is given by [12] y = Σ H Σ G V h G x + n, (3) where Σ H and Σ G are diagonal matrices containing the singular values of H, G, respectively and V G is the matrix of the right singular vectors of G. When LDPC is employed in this MIMO system, the overall utilization in b/s/Hz is determined by the mutual information between the transmitting branches x and the receiving ones, y [6], [7]. It is shown [12] that the mutual information between x and y, I(x; y), is only a function of W "
##### Article: Linear Precoding for MIMO Channels with QAM Constellations and Reduced Complexity
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ABSTRACT: In this paper, the problem of designing a linear precoder for Multiple-Input Multiple-Output (MIMO) systems in conjunction with Quadrature Amplitude Modulation (QAM) is addressed. First, a novel and efficient methodology to evaluate the input-output mutual information for a general Multiple-Input Multiple-Output (MIMO) system as well as its corresponding gradients is presented, based on the Gauss-Hermite quadrature rule. Then, the method is exploited in a block coordinate gradient ascent optimization process to determine the globally optimal linear precoder with respect to the MIMO input-output mutual information for QAM systems with relatively moderate MIMO channel sizes. The proposed methodology is next applied in conjunction with the complexity-reducing per-group processing (PGP) technique, which is semi-optimal, to both perfect channel state information at the transmitter (CSIT) as well as statistical channel state information (SCSI) scenarios, with high transmitting and receiving antenna size, and for constellation size up to $M=64$. We show by numerical results that the precoders developed offer significantly better performance than the configuration with no precoder, and the maximum diversity precoder for QAM with constellation sizes $M=16,~32$, and $~64$ and for MIMO channel size $100\times100$.
Full-text · Article · Feb 2016
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• "In this work, we analytically study the criterion for matching 44 the source statistics with source coding rate using an innovative 45 PEXIT chart technique. EXIT chart [11] is an accurate and con-46 venient tool for predicting the performance of LDPC codes. It 47 was introduced into D-LDPC code systems in [1] and extended 48 to P-LDPC codes in [12] as PEXIT chart. "
##### Article: Matching Criterion betweenthe Source Statistics and Source Coding Rate

Full-text · Article · Sep 2015 · IEEE Wireless Communication Letters
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• "In this work, we analytically study the criterion for matching 44 the source statistics with source coding rate using an innovative 45 PEXIT chart technique. EXIT chart [11] is an accurate and con-46 venient tool for predicting the performance of LDPC codes. It 47 was introduced into D-LDPC code systems in [1] and extended 48 to P-LDPC codes in [12] as PEXIT chart. "
##### Article: Matching Criterion Between Source Statistics and Source Coding Rate
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ABSTRACT: Joint source–channel coding (JSCC) based on double protograph low-density parity-check (DP-LDPC) codes has been shown to be a good solution for wireless communications. However, the premature error floor region of the DP-LDPC codes usually does not meet the bit-error-rate requirements. In this letter, we provide a matching criterion between the source statistics and the source coding rate using a novel protograph extrinsic information transfer (PEXIT) algorithm with a new decoding threshold. The resulting matching criterion helps predict the error floor region performance and give directions for source coding rate designs.
Full-text · Article · Sep 2015 · IEEE Wireless Communication Letters