Performance of low-density generator matrix codes on perpendicular recording channels

We examine the performance of a rate-0.9 structured irregular repeat-accumulate (S-IRA) code on a perpendicular magnetic recording (PMR) channel with media noise. To account for the presence of data-dependent media noise, a pattern-dependent-noise-predictive (PDNP) channel detector is employed, in which the prediction filters are trained using the LMS algorithm. We compare the error rate performance of the S-IRA code with that of a Reed-Solomon (RS) code of the same length and rate, with the PDNP detector present in both cases. Our results show that the S-IRA code achieves a gain of over 1 dB relative to the RS code for sector error rates down past 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-4</sup> , but only if the columns of its H-matrix are properly permuted. We have also estimated that the linear density gain attainable by the S-IRA code relative to the RS code is about 8% for the operating point we have chosen.

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.

We present a ternary source coding scheme in this paper, which is a special class of low density generator matrix (LDGM) codes. We prove that a ternary linear block LDGM code, whose generator matrix is randomly generated with each element independent and identically distributed, is universal for source coding in terms of the symbol-error rate (SER). To circumvent the high-complex maximum likelihood decoding, we introduce a special class of convolutional LDGM codes, called block Markov superposition transmission of repetition (BMST-R) codes, which are iteratively decodable by a sliding window algorithm. Then the presented BMST-R codes are applied to construct a tandem scheme for Gaussian source compression, where a dead-zone quantizer is introduced before the ternary source coding. The main advantages of this scheme are its universality and flexibility. The dead-zone quantizer can choose a proper quantization level according to the distortion requirement, while the LDGM codes can adapt the code rate to approach the entropy of the quantized sequence. Numerical results show that the proposed scheme performs well for ternary sources over a wide range of code rates and that the distortion introduced by quantization dominates provided that the code rate is slightly greater than the discrete entropy.

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

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.

The long-term bit error rate (BER) performance of partial response maximum likelihood (PRML) system in a perpendicular magnetic recording (PMR) channel with thermal decay is studied. A thermal decay model based on the experimental data for three CoPtCr-SiO2 PMR media with different thermal stability is obtained. Then, the performance of PR1ML channel for the 16/17(0,6/6) and 128/130(0,16/8) codes as a run-length-limited (RLL) code is evaluated by computer simulation using the model. Moreover, the relationships between the elapsed time and the BER are obtained for the combinations of two RLL codes and three PMR media and their performances are compared. The results show that for the combination of the 128/130(0,16/8) code and the medium with the poorest thermal stability, the degradation with the elapsed time is noticeable compared with the other combinations

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.

This paper proposes a jitter-sensitive-sequence-detection scheme based on a realistic transition noise model for high-density perpendicular magnetic recording channels. In this scheme, the transition jitter is assumed to have one of the Q discrete values, and the discretized jitter sequence is estimated jointly with the recorded bit sequence using maximum a posteriori criterion. The detection performance is compared with that of the pattern dependent noise predictive scheme based on an autoregressive Gaussian noise model. Simulation results show that the scheme provides a significant gain when the transition jitter is large and the resulting transition noise dominates over the electronic noise.

Towards the goal of achieving better error correction performance in data storage systems, iterative soft decoding of low density parity check (LDPC) codes and soft-decision decoding of Reed-Solomon (RS) codes have started receiving increasing research attention. However, even with increased computing power, complexities of soft-decision decoding algorithms are still too high for real products which require high throughput and small hardware area. Another problem is that the performance gains of those approaches are smaller for magnetic recording channels than they are for memoryless additive white Gaussian noise (AWGN) channels. We propose a new soft-decision decoding algorithm (based on the Chase algorithm), which takes advantage of pattern reliability instead of symbol reliability or bit reliability. We also present a modified Viterbi algorithm that provides probable error patterns with corresponding reliabilities. Simulation results of the proposed algorithms over the partial response (PR) channel show attractive performance gains. The proposed algorithm dramatically reduces the number of iterations compared to the conventional Chase2 algorithm over the PR channel.

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.

Coding Schemes for Energy Constrained IoT Devices

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.

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 proposes a finite-precision decoding method for low-density parity-check (LDPC) codes that features the three steps of Reconstruction, Computation, and Quantization (RCQ). Unlike Mutual-Information-Maximization Quantized Belief Propagation (MIM-QBP), RCQ can approximate either belief propagation or Min-Sum decoding. MIM-QBP decoders do not work well when the fraction of degree-2 variable nodes is large. However, sometimes a large fraction of degree-2 variable nodes is used to facilitate a fast encoding structure, as seen in the IEEE 802.11 standard and the DVB-S2 standard. In contrast to MIM-QBP, the proposed RCQ decoder may be applied to any off-the-shelf LDPC code, including those with a large fraction of degree-2 variable nodes. Simulations show that a 4-bit Min-Sum RCQ decoder delivers frame error rate (FER) performance within 0.1 dB of floating point belief propagation (BP) for the IEEE 802.11 standard LDPC code in the low SNR region. The RCQ decoder actually outperforms floating point BP and Min-Sum in the high SNR region were FER less than 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-5</sup> . This paper also introduces Hierarchical Dynamic Quantization (HDQ) to design the time-varying non-uniform quantizers required by RCQ decoders. HDQ is a low-complexity design technique that is slightly sub-optimal. Simulation results comparing HDQ and optimal quantization on the symmetric binary-input memoryless additive white Gaussian noise channel show a mutual information loss of less than 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-6</sup> bits, which is negligible in practice.