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

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

On Universal Properties of Capacity-Approaching LDPC 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.Comment: Published in the IEEE Trans. on Information Theory, vol. 55, no. 7, pp. 2956 - 2990, July 200

One and Two Bit Message Passing for SC-LDPC Codes with Higher-Order Modulation

Low complexity decoding algorithms are necessary to meet data rate requirements in excess of 1 Tbps. In this paper, we study one and two bit message passing algorithms for belief propagation decoding of low-density parity-check (LDPC) codes and analyze them by density evolution. The variable nodes (VNs) exploit soft information from the channel output. To decrease the data flow, the messages exchanged between check nodes (CNs) and VNs are represented by one or two bits. The newly proposed quaternary message passing (QMP) algorithm is compared asymptotically and in finite length simulations to binary message passing (BMP) and ternary message passing (TMP) for spectrally efficient communication with higher-order modulation and probabilistic amplitude shaping (PAS). To showcase the potential for high throughput forward error correction, spatially coupled LDPC codes and a target spectral efficiency (SE) of 3 bits/QAM symbol are considered. Gains of about 0.7 dB and 0.1 dB are observed compared to BMP and TMP, respectively. The gap to unquantized belief propagation (BP) decoding is reduced to about 0.75 dB. For smaller code rates, the gain of QMP compared to TMP is more pronounced and amounts to 0.24 dB in the considered example.Comment: Accepted for IEEE/OSA Journal on Lightwave Technolog

Fountain Codes under Maximum Likelihood Decoding

This dissertation focuses on fountain codes under maximum likelihood (ML) decoding. First LT codes are considered under a practical and widely used ML decoding algorithm known as inactivation decoding. Different analysis techniques are presented to characterize the decoding complexity. Next an upper bound to the probability of decoding failure of Raptor codes under ML decoding is provided. Then, the distance properties of an ensemble of fixed-rate Raptor codes with linear random outer codes are analyzed. Finally, a novel class of fountain codes is presented, which consists of a parallel concatenation of a block code with a linear random fountain code.Comment: PhD Thesi