Capacity-approaching Low-density Parity-check Research Articles

Pareto Optimization of Adaptive Modulation and Coding Set in Nonlinear Fiber-Optic Systems

In recent coherent optical communications, various high-order modulation formats have been used in conjunction with soft-decision forward error correction (FEC) such as capacity-approaching low-density parity-check (LDPC) codes. With a proper selection of modulation order and FEC overhead, we may be able to achieve the highest spectral efficiency (SE) for a given fiber plant configuration. However, it is often not straightforward to select the best pair of modulation format and FEC overhead due to many factors, including fiber nonlinearity, channel spacing, baud rates, communications distance, link budget, and power consumption. In this paper, we introduce a new framework to design adaptive modulation and coding (AMC) sets based on Pareto efficiency in order to optimize multiple objective functions, more specifically, to achieve higher SE, higher nonlinearity tolerance, and lower power consumption at the same time. We compare various modulation formats and variable-rate LDPC codes based on generalized mutual information (GMI) in nonlinear fiber transmissions. In order to account for the penalty of finite-iteration decoding under a constraint of power consumption, we use required GMI as a new metric for AMC design. With our AMC framework, Pareto-efficient pairs of modulation and coding can be identified to achieve both higher SE and higher nonlinearity tolerance constrained on power consumption.

EXIT-Chart-Based LDPC Code Design for 2D ISI Channels

In this paper, optimization of low-density parity-check (LDPC) codes to approach the symmetric information rate (SIR) of two-dimensional (2-D) intersymbol interference (ISI) channels is proposed for high-density magnetic recording, such as bit-patterned magnetic recording (BPMR) and 2-D magnetic recording (TDMR). The code design makes use of the modified Extrinsic Information Transfer (EXIT) chart, where the optimal variable node degree is searched by selecting the best check node degree to fit the check node decoder (CND) EXIT curve to the EXIT curve of the variable node decoder (VND) curve combined with 2-D detector. Simulation results show that LDPC codes with code length 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sup> bits optimized for a 2-D ISI channel corresponding to 4 Tb/in <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> recording density can achieve bit error rate 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-5</sup> at signal-to-noise ratio 0.33 dB away from the SIR. To our knowledge, this is the first capacity-approaching LDPC code successfully optimized for a 2-D ISI channel.

Decoding and Design of LDPC Codes for High-Order Modulations

A concatenated code model is proposed for high-order low-density parity-check (LDPC) coded modulations. A corresponding concatenated-code belief propagation (CCBP) decoding algorithm is derived for our proposed concatenated code. Moreover, the design of LDPC codes under the CCBP decoding is developed using extrinsic information transfer (EXIT) charts. Compared with other algorithms, the CCBP method provides an excellent parallel decoding process, and the EXIT-based design method offers highly accurate LDPC code ensembles. Simulation results show that the performance of the proposed CCBP algorithm is superior to that of the conventional belief propagation decoding within a wide range of modulation orders, and the EXIT-based method can design capacity-approaching LDPC codes for high-order modulations.

On Universal Properties of Capacity-Approaching LDPC Code Ensembles

This paper is focused on the derivation of some universal properties of capacity-approaching low-density parity-check (LDPC) code ensembles whose transmission takes place over memoryless binary-input output-symmetric (MBIOS) channels. Properties of the degree distributions, graphical complexity and the number of fundamental cycles in the bipartite graphs are considered via the derivation of information-theoretic bounds. These bounds are expressed in terms of the target block/ bit error probability and the gap (in rate) to capacity. Most of the bounds are general for any decoding algorithm, and some others are proved under belief propagation (BP) decoding. Proving these bounds under a certain decoding algorithm, validates them automatically also under any sub-optimal decoding algorithm. A proper modification of these bounds makes them universal for the set of all MBIOS channels which exhibit a given capacity. Bounds on the degree distributions and graphical complexity apply to finite-length LDPC codes and to the asymptotic case of an infinite block length. The bounds are compared with capacity-approaching LDPC code ensembles under BP decoding, and they are shown to be informative and are easy to calculate. Finally, some interesting open problems are considered.

Multiuser Detection of Sparsely Spread CDMA

Code-division multiple access (CDMA) is the basis of a family of advanced air interfaces in current and future generation networks. The benefits promised by CDMA have not been fully realized partly due to the prohibitive complexity of optimal detection and decoding of many users communicating simultaneously using the same frequency band. From both theoretical and practical perspectives, this paper advocates a new paradigm of CDMA with sparse spreading sequences, which enables near-optimal multiuser detection using belief propagation (BP) with low-complexity. The scheme is in part inspired by capacity-approaching low-density parity-check (LDPC) codes and the success of iterative decoding techniques. Specifically, it is shown that BP-based detection is optimal in the large-system limit under many practical circumstances, which is a unique advantage of sparsely spread CDMA systems. Moreover, it is shown that, from the viewpoint of an individual user, the CDMA channel is asymptotically equivalent to a scalar Gaussian channel with some degradation in the signal-to-noise ratio (SNR). The degradation factor, known as the multiuser efficiency, can be determined from a fixed-point equation. The results in this paper apply to a broad class of sparse, semi-regular CDMA systems with arbitrary input and power distribution. Numerical results support the theoretical findings for systems of moderate size, which further demonstrate the appeal of sparse spreading in practical applications.