Degree Distribution Pair Research Articles

Optimisation of convergence‐aware coded PDMA for 5G wireless systems

Orthogonal frequency division multiplexing-based pattern division multiple access (PDMA) is considered as a promising multiple access scheme for future wireless communication systems due to its high spectral efficiency and powerful ability to support massive users. In this study, it is shown that two pattern matrices with unequal diversity gain in the PDMA system have better convergence performance compared with the signature matrices in a traditional low-density signature multiple access system by simulations and extrinsic information transfer (EXIT) chart analysis. For a low-density parity check (LDPC)-coded PDMA system, the EXIT characteristics between the front-end multiple-user detector (MUD) and the LDPC decoder may be mismatch, which usually leads to degraded performance when an iterative detection and decoding algorithm is used. To overcome this problem, a two-stage iterative optimisation algorithm, which is easy to implement is proposed to find an optimal (near optimal) degree distribution pair for the LDPC code. Both EXIT chart analysis and simulation results demonstrate that the proposed algorithm exhibits further performance gain compared with regular (3,6) LDPC-coded systems under both an additive white Gaussian noise channel and a Rayleigh fading channel.

Novel Construction and Optimization of LDPC Codes for NC-OFDM Cognitive Radio Systems

In this paper, a random Low-Density Parity-Check (LDPC) code is proposed for Noncontiguous Orthogonal Frequency Division Multiplexing (NC-OFDM) Cognitive Radio (CR) systems. Unlike other encoding schemes which achieve a system code rate of only 1/4 when half of the subcarriers are active, the proposed scheme achieves a system code rate of 1/2. The LDPC code is used to enhance the data transmission rate. A new channel model comprised of a binary erasure channel concatenated with an uncorrelated fading channel and an AWGN channel is adopted for NC-OFDM CR systems. Moreover, the adopted channel model is employed with density evolution algorithm to obtain good degree distribution pairs for the LDPC code. Thereafter, a modified shortest-path algorithm is used to construct the parity-check matrix for the LDPC code. Simulation results show that the proposed LDPC code performs well in terms of both error rate and data transmission rate.

Strong Secrecy on the Binary Erasure Wiretap Channel Using Large-Girth LDPC Codes

For an arbitrary degree distribution pair (DDP), we construct a sequence of low-density parity-check (LDPC) code ensembles with girth growing logarithmically in block-length using Ramanujan graphs. When the DDP has minimum left degree at least three, we show using density evolution analysis that the expected bit-error probability of these ensembles, when passed through a binary erasure channel with erasure probability $\epsilon$, decays as $\mathcal{O}(\exp(-c_1 n^{c_2}))$ with the block-length $n$ for positive constants $c_1$ and $c_2$, as long as $\epsilon$ is lesser than the erasure threshold $\epsilon_\mathrm{th}$ of the DDP. This guarantees that the coset coding scheme using the dual sequence provides strong secrecy over the binary erasure wiretap channel for erasure probabilities greater than $1 - \epsilon_\mathrm{th}$.

Weight Distribution of Low-Density Parity-Check Codes

We derive the average weight distribution function and its asymptotic growth rate for low-density parity-check (LDPC) code ensembles. We show that the growth rate of the minimum distance of LDPC codes depends only on the degree distribution pair. It turns out that capacity-achieving sequences of standard (unstructured) LDPC codes under iterative decoding over the binary erasure channel (BEC) known to date have sublinearly growing minimum distance in the block length

Irregular low-density parity-check codes: construction and performance on perpendicular magnetic recording channels

In this paper, we propose an algorithm to design an irregular low-density parity-check code (LDPC), with a given degree distribution pair, from a random regular LDPC code. The proposed algorithm splits columns and rows of the regular code in order to achieve the desired degree distribution pair. Kou, Lin, and Fossorier have used column splitting to increase code rate. However, we use the splitting technique to achieve a given degree distribution pair in the bipartite graph of the resultant irregular code. The bit-error rate (BER) performance of high-rate irregular LDPC codes, constructed using this algorithm, were simulated on equalized perpendicular magnetic recording channels. In addition, this paper compares the performance of these irregular codes with that of random regular LDPC codes.

Capacity-approaching bandwidth-efficient coded modulation schemes based on low-density parity-check codes

We design multilevel coding (MLC) and bit-interleaved coded modulation (BICM) schemes based on low-density parity-check (LDPC) codes. The analysis and optimization of the LDPC component codes for the MLC and BICM schemes are complicated because, in general, the equivalent binary-input component channels are not necessarily symmetric. To overcome this obstacle, we deploy two different approaches: one based on independent and identically distributed (i.i.d.) channel adapters and the other based on coset codes. By incorporating i.i.d. channel adapters, we can force the symmetry of each binary-input component channel. By considering coset codes, we extend the concentration theorem based on previous work by Richardson et al. ( see ibid., vol.47, p.599-618, Feb. 2001) and Kavc/spl caron/ic/spl acute/ et al.(see ibid., vol.49, p.1636-52, July 2003) We also discuss the relation between the systems based on the two approaches and show that they indeed have the same expected decoder behavior. Next, we jointly optimize the code rates and degree distribution pairs of the LDPC component codes for the MLC scheme. The optimized irregular LDPC codes at each level of MLC with multistage decoding (MSD) are able to perform well at signal-to-noise ratios (SNR) very close to the capacity of the additive white Gaussian noise (AWGN) channel. We also show that the optimized BICM scheme can approach the parallel independent decoding (PID) capacity as closely as does the MLC/PID scheme. Simulations with very large codeword length verify the accuracy of the analytical results. Finally, we compare the simulated performance of these coded modulation schemes at finite codeword lengths, and consider the results from the perspective of a random coding exponent analysis.