Protograph-Based LDPC Code Design for Probabilistic Shaping with On-Off Keying

This work investigates protograph-based LDPC codes for the AWGN channel with OOK modulation. A non-uniform distribution of the OOK modulation symbols is considered to improve the power efficiency especially for low SNRs. To this end, a specific transmitter architecture based on time sharing is proposed that allows probabilistic shaping of (some) OOK modulation symbols. Tailored protograph-based LDPC code designs outperform standard schemes with uniform signaling and off-the-shelf codes by 1.1 dB for a transmission rate of 0.25 bits/channel use.Comment: Invited Paper for CISS 201

Improving soft FEC performance for higher-order modulations via optimized bit channel mappings

Soft forward error correction with higher-order modulations is often implemented in practice via the pragmatic bit-interleaved coded modulation paradigm, where a single binary code is mapped to a nonbinary modulation. In this paper, we study the optimization of the mapping of the coded bits to the modulation bits for a polarization-multiplexed fiber-optical system without optical inline dispersion compensation. Our focus is on protograph-based low-density parity-check (LDPC) codes which allow for an efficient hardware implementation, suitable for high-speed optical communications. The optimization is applied to the AR4JA protograph family, and further extended to protograph-based spatially coupled LDPC codes assuming a windowed decoder. Full field simulations via the split-step Fourier method are used to verify the analysis. The results show performance gains of up to 0.25 dB, which translate into a possible extension of the transmission reach by roughly up to 8%, without significantly increasing the system complexity.Comment: This paper was published in Optics Express and is made available as an electronic reprint with the permission of OSA. The paper can be found at the following URL on the OSA website: http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-22-12-1454

Spatially Coupled LDPC Codes Constructed from Protographs

In this paper, we construct protograph-based spatially coupled low-density parity-check (SC-LDPC) codes by coupling together a series of L disjoint, or uncoupled, LDPC code Tanner graphs into a single coupled chain. By varying L, we obtain a flexible family of code ensembles with varying rates and frame lengths that can share the same encoding and decoding architecture for arbitrary L. We demonstrate that the resulting codes combine the best features of optimized irregular and regular codes in one design: capacity approaching iterative belief propagation (BP) decoding thresholds and linear growth of minimum distance with block length. In particular, we show that, for sufficiently large L, the BP thresholds on both the binary erasure channel (BEC) and the binary-input additive white Gaussian noise channel (AWGNC) saturate to a particular value significantly better than the BP decoding threshold and numerically indistinguishable from the optimal maximum a-posteriori (MAP) decoding threshold of the uncoupled LDPC code. When all variable nodes in the coupled chain have degree greater than two, asymptotically the error probability converges at least doubly exponentially with decoding iterations and we obtain sequences of asymptotically good LDPC codes with fast convergence rates and BP thresholds close to the Shannon limit. Further, the gap to capacity decreases as the density of the graph increases, opening up a new way to construct capacity achieving codes on memoryless binary-input symmetric-output (MBS) channels with low-complexity BP decoding.Comment: Submitted to the IEEE Transactions on Information Theor

Quasi-Cyclic Asymptotically Regular LDPC Codes

Families of "asymptotically regular" LDPC block code ensembles can be formed by terminating (J,K)-regular protograph-based LDPC convolutional codes. By varying the termination length, we obtain a large selection of LDPC block code ensembles with varying code rates, minimum distance that grows linearly with block length, and capacity approaching iterative decoding thresholds, despite the fact that the terminated ensembles are almost regular. In this paper, we investigate the properties of the quasi-cyclic (QC) members of such an ensemble. We show that an upper bound on the minimum Hamming distance of members of the QC sub-ensemble can be improved by careful choice of the component protographs used in the code construction. Further, we show that the upper bound on the minimum distance can be improved by using arrays of circulants in a graph cover of the protograph.Comment: To be presented at the 2010 IEEE Information Theory Workshop, Dublin, Irelan

Protograph-Based LDPC Code Design for Shaped Bit-Metric Decoding

A protograph-based low-density parity-check (LDPC) code design technique for bandwidth-efficient coded modulation is presented. The approach jointly optimizes the LDPC code node degrees and the mapping of the coded bits to the bit-interleaved coded modulation (BICM) bit-channels. For BICM with uniform input and for BICM with probabilistic shaping, binary-input symmetric-output surrogate channels for the code design are used. The constructed codes for uniform inputs perform as good as the multi-edge type codes of Zhang and Kschischang (2013). For 8-ASK and 64-ASK with probabilistic shaping, codes of rates 2/3 and 5/6 with blocklength 64800 are designed, which operate within 0.63dB and 0.69dB of continuous AWGN capacity for a target frame error rate of 1e-3 at spectral efficiencies of 1.38 and 4.25 bits/channel use, respectively.Comment: 9 pages, 10 figures. arXiv admin note: substantial text overlap with arXiv:1501.0559

Analysis of Quasi-Cyclic LDPC codes under ML decoding over the erasure channel

In this paper, we show that Quasi-Cyclic LDPC codes can efficiently accommodate the hybrid iterative/ML decoding over the binary erasure channel. We demonstrate that the quasi-cyclic structure of the parity-check matrix can be advantageously used in order to significantly reduce the complexity of the ML decoding. This is achieved by a simple row/column permutation that transforms a QC matrix into a pseudo-band form. Based on this approach, we propose a class of QC-LDPC codes with almost ideal error correction performance under the ML decoding, while the required number of row/symbol operations scales as $k\sqrt{k}$, where $k$ is the number of source symbols.Comment: 6 pages, ISITA1