This paper estimates threshold values of the message-passing iterative decoder for expander codes on discrete-input additive white Gaussian noise (AWGN) channels. We give a new upper bound on the rate of these codes and argue that expander codes are good codes at high rates on this channel.
We study the limits of performance of Gallager codes (low-density parity-check (LDPC) codes) over binary linear intersymbol interference (ISI) channels with additive white Gaussian noise (AWGN). Using the graph representations of the channel, the code, and the sum-product message-passing detector/decoder, we prove two error concentration theorems. Our proofs expand on previous work by handling complications introduced by the channel memory. We circumvent these problems by considering not just linear Gallager codes but also their cosets and by distinguishing between different types of message flow neighborhoods depending on the actual transmitted symbols. We compute the noise tolerance threshold using a suitably developed density evolution algorithm and verify, by simulation, that the thresholds represent accurate predictions of the performance of the iterative sum-product algorithm for finite (but large) block lengths. We also demonstrate that for high rates, the thresholds are very close to the theoretical limit of performance for Gallager codes over ISI channels. If C denotes the capacity of a binary ISI channel and if C/sub i.i.d./ denotes the maximal achievable mutual information rate when the channel inputs are independent and identically distributed (i.i.d.) binary random variables (C/sub i.i.d.//spl les/C), we prove that the maximum information rate achievable by the sum-product decoder of a Gallager (coset) code is upper-bounded by C/sub i.i.d./. The last topic investigated is the performance limit of the decoder if the trellis portion of the sum-product algorithm is executed only once; this demonstrates the potential for trading off the computational requirements and the performance of the decoder.
This paper investigates about the usefulness of some recently published low complexity upper bounds on belief-propagation decoding thresholds for irregular low-density parity-check (LDPC) codes to analyze their performance on memoryless binary input - additive white Gaussian noise (BI-AWGN) channels, with sum-product decoding. Irregular LDPC codes are known to perform better than regular ones, and to exhibit, like them, the so called “threshold phenomenon”, being the threshold defined as the maximum noise level such that an arbitrarily small bit-error probability can be achieved as the block length tends to infinity. We use a simplified analysis of the belief-propagation decoding algorithm, i.e., consider a Gaussian approximation for message densities under density evolution, and a simple algorithmic method, defined recently, to estimate the decoding thresholds for regular and irregular LDPC codes on BI-AWGN channels.
A noisy message-passing decoding scheme isconsidered for low-density parity-check (LDPC) codes overadditive white Gaussian noise (AWGN) channels. The internaldecoder noise is motivated by the quantization noise in digitalimplementations or the intrinsic noise of analog LDPC decoders.We modelled the decoder noise as AWGN on the exchangedmessages in the iterative LDPC decoder. This is shown to renderthe message densities in the noisy LDPC decoder inconsistent.We then invoke Gaussian approximation and formulate a twodimensionaldensity evolution analysis for the noisy LDPCdecoder. This allows for not only tracking the mean, but also thevariance of the message densities, and hence, quantifying thethreshold of the LDPC code. According to the results, a decodernoise of unit variance, increases the threshold for a regular (3,6) code by 1.672dB.
We address noisy message-passing decoding of lowdensity parity-check (LDPC) codes over additive white Gaussian noise channels. Message-passing decoders in which certain processing units iteratively exchange messages are common for decoding LDPC codes. The exchanged messages are in general subject to internal noise in hardware implementation of these decoders. We model the internal decoder noise as additive white Gaussian noise (AWGN) degrading exchanged messages. Using Gaussian approximation of the exchanged messages, we perform a two-dimensional density evolution analysis for the noisy LDPC decoder. This makes it possible to track both the mean, and the variance of the exchanged message densities, and hence, to quantify the threshold of the LDPC code in the presence of internal decoder noise. The numerical and simulation results are presented that quantify the performance loss due to the internal decoder noise. To partially compensate this performance loss, we propose a simple method, based on EXIT chart analysis, to design robust irregular LDPC codes. The simulation results indicate that the designed codes can indeed compensate part of the performance loss due to the internal decoder noise.
Focus of this letter is the oldest class of codes that can approach the Shannon limit quite closely, i.e., low-density parity-check (LDPC) codes, and two mathematical tools that can make their design an easier job under appropriate assumptions. In particular, we present a simple algorithmic method to estimate the threshold for regular and irregular LDPC codes on memoryless binary-input continuous-output additive white Gaussian noise (AWGN) channels with sum-product decoding, and, to determine how close are the obtained thresholds to the theoretical maximum, i.e., to the Shannon limit, we give a simple and invertible expression of the AWGN channel capacity in the binary input-soft output case. For these codes, the thresholds are defined as the maximum noise level, such that an arbitrarily small bit-error probability can be achieved as the block length tends to infinity. We assume a Gaussian approximation for message densities under density evolution, a widely used simplification of the decoding algorithm.
The theoretical performance of binary codes for the additive white Gaussian noise (AWGN) channel is discussed. In particular, Gallager’s coding theorem for binary codes is treated extensively. By assuming a binomial weight distribution for linear codes, it is shown that the decoder error probability performance of some of the best, known linear, binary codes is the same as the average performance of the ensemble of all randomly chosen, binary nonlinear codes having the same length and dimension. Assuming a binomial weight distribution, an upper bound is determined for the erasure performance of any code, and it is shown that this can be translated into an upper bound for code performance in the AWGN channel. Finally, theoretical bounds on the construction of error-correction codes are discussed. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.