Finite-Length Performance Analysis of LDPC Coded Continuous Phase Modulation

Serial concatenation of LDPC codes and continuous phase modulation (CPM) has recently gained significant attention due to its capacity-approaching performance, efficient detection as well as owing to its constant-envelope nature. Most of the previous contributions on LDPC coded CPM were devoted to the design of LDPC codes and their asymptotic performance analysis. However, there is a paucity of work on the finite-length performance estimation of LDPC coded CPM, primarily because existing performance estimation techniques cannot be readily applied to the LDPC coded CPM. To fill this gap, we conceive an analytical bit error probability estimation technique for finite-length LDPC coded CPM in the waterfall region. Numerical results are provided both for regular and irregular LDPC codes having different codeword lengths, demonstrating that the estimated performances are closely matched by the simulated ones

Finite-length performance analysis of LDPC coded continuous phase modulation

Serial concatenation of LDPC codes and continuous phase modulation (CPM) has recently gained significant attention due to its capacity-approaching performance, efficient detection as well as owing to its constant-envelope nature. Most of the previous contributions on LDPC coded CPM were devoted to the design of LDPC codes and their asymptotic performance analysis. However, there is a paucity of work on the finite-length performance estimation of LDPC coded CPM, primarily because existing performance estimation techniques cannot be readily applied to the LDPC coded CPM. To fill this gap, we conceive an analytical bit error probability estimation technique for finite-length LDPC coded CPM in the waterfall region. Numerical results are provided both for regular and irregular LDPC codes having different codeword lengths, demonstrating that the estimated performances are closely matched by the simulated ones

Low-Complexity LP Decoding of Nonbinary Linear Codes

Linear Programming (LP) decoding of Low-Density Parity-Check (LDPC) codes has attracted much attention in the research community in the past few years. LP decoding has been derived for binary and nonbinary linear codes. However, the most important problem with LP decoding for both binary and nonbinary linear codes is that the complexity of standard LP solvers such as the simplex algorithm remains prohibitively large for codes of moderate to large block length. To address this problem, two low-complexity LP (LCLP) decoding algorithms for binary linear codes have been proposed by Vontobel and Koetter, henceforth called the basic LCLP decoding algorithm and the subgradient LCLP decoding algorithm. In this paper, we generalize these LCLP decoding algorithms to nonbinary linear codes. The computational complexity per iteration of the proposed nonbinary LCLP decoding algorithms scales linearly with the block length of the code. A modified BCJR algorithm for efficient check-node calculations in the nonbinary basic LCLP decoding algorithm is also proposed, which has complexity linear in the check node degree. Several simulation results are presented for nonbinary LDPC codes defined over Z_4, GF(4), and GF(8) using quaternary phase-shift keying and 8-phase-shift keying, respectively, over the AWGN channel. It is shown that for some group-structured LDPC codes, the error-correcting performance of the nonbinary LCLP decoding algorithms is similar to or better than that of the min-sum decoding algorithm.Comment: To appear in IEEE Transactions on Communications, 201

Windowed Decoding of Protograph-based LDPC Convolutional Codes over Erasure Channels

We consider a windowed decoding scheme for LDPC convolutional codes that is based on the belief-propagation (BP) algorithm. We discuss the advantages of this decoding scheme and identify certain characteristics of LDPC convolutional code ensembles that exhibit good performance with the windowed decoder. We will consider the performance of these ensembles and codes over erasure channels with and without memory. We show that the structure of LDPC convolutional code ensembles is suitable to obtain performance close to the theoretical limits over the memoryless erasure channel, both for the BP decoder and windowed decoding. However, the same structure imposes limitations on the performance over erasure channels with memory.Comment: 18 pages, 9 figures, accepted for publication in the IEEE Transactions on Information Theor

Ultra-Sparse Non-Binary LDPC Codes for Probabilistic Amplitude Shaping

This work shows how non-binary low-density parity-check codes over GF($2^p$) can be combined with probabilistic amplitude shaping (PAS) (B\"ocherer, et al., 2015), which combines forward-error correction with non-uniform signaling for power-efficient communication. Ultra-sparse low-density parity-check codes over GF(64) and GF(256) gain 0.6 dB in power efficiency over state-of-the-art binary LDPC codes at a spectral efficiency of 1.5 bits per channel use and a blocklength of 576 bits. The simulation results are compared to finite length coding bounds and complemented by density evolution analysis.Comment: Accepted for Globecom 201