Ternary Convolutional LDGM Codes with Applications to Gaussian Source Compression

We investigate rate-adaptive continuous phase modulation (CPM) with punctured low-density generator matrix (LDGM) codes. We give an adaptive principal component analysis (PCA) CPM receiver for slow-fading channels. With the merit of the PCA receiver, the new receiver avoids the eigenvalue decomposition in every symbol interval, and uses a fixed filter-bank. By changing the rate of the LDGM codes, the information rate of CPM signals is adapted to the channel state information (CSI). We use a low rate LDGM code as the mother code, and higher rates are achieved by puncturing the output of the LDGM codes. To exploit the rate-flexible property of punctured LDGM codes, a rate function is proposed to calculate the rate of each transmitted block. Thus, we can have a quasi-continuous information rate. Numerical results for MSK show that up to 11 dB transmitted energy gain can be achieved in the low bit-error-rate region (smaller than 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3</sup> ), compared to the non-adaptive systems

This paper presents three new ensembles of low density generator matrix (LDGM) codes, all of which are systematic codes. We prove that, under the maximum likelihood (ML) decoding, these codes can achieve the capacity of binary-input output-symmetric (BIOS) memoryless channels in terms of bit-error rate (BER). The proof technique is different from that for totally random block code ensembles. The recently proposed systematic block Markov superposition (BMST) code is treated as a variant of the presented ensembles, exhibiting capacity approaching performance with iterative belief propagation decoding algorithm.

We propose a new transmission scheme of multi-rate low density generator matrix (LDGM) code suitable for optical satellite communications. Since the proposed scheme doesn't utilize a preamble transmission of the rate information nor the repeat request scheme, a long feedback delay in the satellite link and a decrease of transmission efficiency can be avoided. Then, an adaptive rate transmission only with forward error correction (FEC) is achieved and the transmitter can choose the quality or the rate-efficiency of transmission from the transmitter-side state. In the receiver, an exact rate-decision and decoding are conducted without the preamble. It is shown that the proposed scheme is effective in the satellite-to-ground optical link by the computer simulations.

The application of Low-Density Generator Matrix (LDGM) Codes combined with Survey Propagation (SP) in steganography seems to be advantageous, since it is possible to approximate the coset leader directly. Thus, large codeword length can be applied, resulting in an embedding efficiency close to the theoretical upper bound of embedding efficiency. Since this approach is still quite complex, this paper deals with the application of Belief Propagation (BP) to LDGM Codes used to reduce the complexity of embedding while keeping the embedding efficiency constant.

This paper presents a technique for achieving cooperative spatial diversity using serially concatenated low density generator matrix (LDGM) codes. Specifically, we consider a scenario in which a pair of transceivers employ algebraic superposition of error control codes to effect spatial diversity at their common destination. The construction of LDGM codes from a sparse generator matrix makes them a natural fit for such a cooperative diversity scheme. The simple decoder structure for graph based codes reduces the complexity at the destination compared with previously-proposed schemes using algebraic superposition of convolutional codes and turbo-like decoding. The result is a system with low encoding and decoding complexity and improved error performance.

Cheng (Doctoral Dissertation, CIT, Pasadena, California, 1997) introduced a class of linear codes called low-density generator matrix (LDGM) codes and studied its performance on a memoryless additive white Gaussian noise (AWGN) channel. In this paper, we study its performance on perpendicular magnetic recording channels. The results shown in this paper indicate that the bit-error rate (BER) performance of some LDGM-codes is comparable to that of low-density parity check (LDPC) codes of the same rate.

This paper proposes an extrinsic information transfer (EXIT) chart analysis and an asymptotic bit error rate (BER) prediction method to speed up the design of high rate RCM-LDGM hybrid codes over AWGN and fast Rayleigh channels. These codes are based on a parallel concatenation of a rate compatible modulation (RCM) code with a low-density generator matrix (LDGM) code. The decoder uses the iterative sum-product algorithm to exchange information between the variable nodes (VNs) and the two types of constituent check nodes: RCM-CN and LDGM-CN. The novelty of the proposed EXIT chart procedure lies on the fact that it mixes together the analog RCM check nodes with the digital LDGM check nodes, something not possible in previous multi-edge EXIT charts proposed in the literature.

A new method for analyzing low density parity check (LDPC) codes and low density generator matrix (LDGM) codes under bit maximum a posteriori probability (MAP) decoding is introduced. The method is based on a rigorous approach to spin glasses developed by Francesco Guerra. It allows to construct lower bounds on the entropy of the transmitted message conditional to the received one. Based on heuristic statistical mechanics calculations, we conjecture such bounds to be tight. The result holds for standard irregular ensembles when used over binary input output symmetric channels. The method is first developed for Tanner graph ensembles with Poisson left degree distribution. It is then generalized to `multi-Poisson' graphs, and, by a completion procedure, to arbitrary degree distribution.

This paper focuses on the data fusion scenario where nodes sense and transmit the data generated by a source to a common destination, which estimates the original information from more accurately than in the case of a single sensor. This work joins the upsurge of research interest in this topic by addressing the setup where the sensed information is transmitted over a Gaussian Multiple-Access Channel (MAC). We use Low Density Generator Matrix (LDGM) codes in order to keep the correlation between the transmitted codewords, which leads to an improved received Signal-to-Noise Ratio (SNR) thanks to the constructive signal addition at the receiver front-end. At reception, we propose a joint decoder and estimator that exchanges soft information between the LDGM decoders and a data fusion stage. An error-correcting Bose, Ray-Chaudhuri, Hocquenghem (BCH) code is further applied suppress the error floor derived from the ambiguity of the MAC channel when dealing with correlated sources. Simulation results are presented for several values of and diverse LDGM and BCH codes, based on which we conclude that the proposed scheme outperforms significantly (by up to 6.3 dB) the suboptimum limit assuming separation between Slepian-Wolf source coding and capacity-achieving channel coding.

We investigate the systematic convolutional low density generator matrix (SC-LDGM) codes over Rayleigh fading channels with symmetric alpha-stable (S\(\alpha \)S) impulsive noise. The performance is analyzed by deriving a lower bound based on an equivalent genie-aided (GA) system. Numerical simulations show that the SC-LDGM codes can achieve a significant gain compared to the convolutional codes over Rayleigh fading channels with impulsive noise. Numerical results also show that the performance of the SC-LDGM codes can be around one dB away from Shannon limits at the bit-error rate (BER) of \(10^{-5}\) and matches well with the GA lower bound in the low BER region.

In this paper, we propose a power efficient communication system for linking a brain-implantable device to an external system. For battery powered implantable devices, the processor and the transmitter power should be reduced in order to both conserve battery power and reduce the health risks associated with transmission. To accomplish this, a joint source-channel coding/decoding system is devised. Low-density generator matrix (LDGM) codes are used in our system due to their low encoding complexity. The power cost for signal processing within the implantable device is greatly reduced by avoiding explicit source encoding. Raw data which is highly correlated is transmitted. At the receiver, a Markov chain source correlation model is utilized to approximate and capture the correlation of raw data. A turbo iterative receiver algorithm is designed which connects the Markov chain source model to the LDGM decoder in a turbo-iterative way. Simulation results show that the proposed system can save up to 1 to 2.5 dB on transmission power.

In this paper, we propose an efficient coding scheme for the binary Chief Executive Officer (CEO) problem under logarithmic loss criterion. Courtade and Weissman obtained the exact rate-distortion bound for a two-link binary CEO problem under this criterion. We find optimal parameters of the binary symmetric test-channel model for the encoder of each link by using the given bound. Furthermore, an efficient coding scheme based on compound low-density generator matrix (LDGM)-low-density parity-check (LDPC) codes is presented to achieve the theoretical rates. In the proposed encoding scheme, a binary quantizer using LDGM codes and a syndrome generator using LDPC codes are applied. The proposed decoder employs a sum-product algorithm and a soft estimator to produce an approximate a posteriori distribution of the source bits given the data received through both links. Our numerical examples verify a close performance of the proposed coding scheme to the theoretical bound in several cases.

A low complexity approach for binary quantization is proposed. This approach uses a multi-edge type bipartite graph of the low density generator matrix (LDGM) code with the belief propagation algorithm to encode the informations. A damping decimation is developed for the algorithm convergence. Simulation results show that our algorithm achieves near Shannon capacity performance with reduced complexity.

We study a new encoding scheme for lossy source compression based on spatially coupled low-density generatormatrix codes. We develop a belief-propagation guided-decimation algorithm, and show that this algorithm allows to approach the optimal distortion of spatially coupled ensembles. Moreover, using the survey propagation formalism, we also observe that the optimal distortions of the spatially coupled and individual code ensembles are the same. Since regular low-density generatormatrix codes are known to achieve the Shannon rate-distortion bound under optimal encoding as the degrees grow, our results suggest that spatial coupling can be used to reach the rate-distortion bound, under a low complexity belief-propagation guided-decimation algorithm.

Recently, it has been shown that a class of spatially coupled low-density generator-matrix (SC-LDGM) code ensembles displays distortion saturation for the lossy binary symmetric source coding problem with the belief propagation guided decimation (BPGD) algorithm, i.e., the BPGD distortion approaches the optimal expected distortion of the underlying ensemble asymptotically in code length. Here, we investigate the distortion performance of a practical class of protograph-based SC-LDGM code ensembles and demonstrate distortion saturation numerically. Moreover, we propose an efficient windowed encoding (WE) algorithm that takes advantage of the convolutional structure of the SC-LDGM codes. By using the WE algorithm, a distortion very close to the rate-distortion limit can be achieved for a fixed compression rate with low-to-moderate encoding latency.