Achievable Information Rates for Coded Modulation with Hard Decision Decoding for Coherent Fiber-Optic Systems

We analyze the achievable information rates (AIRs) for coded modulation schemes with QAM constellations with both bit-wise and symbol-wise decoders, corresponding to the case where a binary code is used in combination with a higher-order modulation using the bit-interleaved coded modulation (BICM) paradigm and to the case where a nonbinary code over a field matched to the constellation size is used, respectively. In particular, we consider hard decision decoding, which is the preferable option for fiber-optic communication systems where decoding complexity is a concern. Recently, Liga \emph{et al.} analyzed the AIRs for bit-wise and symbol-wise decoders considering what the authors called \emph{hard decision decoder} which, however, exploits \emph{soft information} of the transition probabilities of discrete-input discrete-output channel resulting from the hard detection. As such, the complexity of the decoder is essentially the same as the complexity of a soft decision decoder. In this paper, we analyze instead the AIRs for the standard hard decision decoder, commonly used in practice, where the decoding is based on the Hamming distance metric. We show that if standard hard decision decoding is used, bit-wise decoders yield significantly higher AIRs than symbol-wise decoders. As a result, contrary to the conclusion by Liga \emph{et al.}, binary decoders together with the BICM paradigm are preferable for spectrally-efficient fiber-optic systems. We also design binary and nonbinary staircase codes and show that, in agreement with the AIRs, binary codes yield better performance.Comment: Published in IEEE/OSA Journal of Lightwave Technology, 201

Binary Message Passing Decoding of Product-like Codes

We propose a novel binary message passing decoding algorithm for product-like codes based on bounded distance decoding (BDD) of the component codes. The algorithm, dubbed iterative BDD with scaled reliability (iBDD-SR), exploits the channel reliabilities and is therefore soft in nature. However, the messages exchanged by the component decoders are binary (hard) messages, which significantly reduces the decoder data flow. The exchanged binary messages are obtained by combining the channel reliability with the BDD decoder output reliabilities, properly conveyed by a scaling factor applied to the BDD decisions. We perform a density evolution analysis for generalized low-density parity-check (GLDPC) code ensembles and spatially coupled GLDPC code ensembles, from which the scaling factors of the iBDD-SR for product and staircase codes, respectively, can be obtained. For the white additive Gaussian noise channel, we show performance gains up to $0.29$ dB and $0.31$ dB for product and staircase codes compared to conventional iterative BDD (iBDD) with the same decoder data flow. Furthermore, we show that iBDD-SR approaches the performance of ideal iBDD that prevents miscorrections.Comment: Accepted for publication in the IEEE Transactions on Communication

Binary Message Passing Decoding of Product Codes Based on Generalized Minimum Distance Decoding

We propose a binary message passing decoding algorithm for product codes based on generalized minimum distance decoding (GMDD) of the component codes, where the last stage of the GMDD makes a decision based on the Hamming distance metric. The proposed algorithm closes half of the gap between conventional iterative bounded distance decoding (iBDD) and turbo product decoding based on the Chase--Pyndiah algorithm, at the expense of some increase in complexity. Furthermore, the proposed algorithm entails only a limited increase in data flow compared to iBDD.Comment: Invited paper to the 53rd Annual Conference on Information Sciences and Systems (CISS), Baltimore, MD, March 2019. arXiv admin note: text overlap with arXiv:1806.1090

Iterative Bounded Distance Decoding of Product Codes with Scaled Reliability

We propose a modified iterative bounded distance decoding of product codes. The proposed algorithm is based on exchanging hard messages iteratively and exploiting channel reliabilities to make hard decisions at each iteration. Performance improvements up to 0.26 dB are achieved

Probabilistically-Shaped Coded Modulation with Hard Decision Decoding for Coherent Optical Systems

We consider probabilistic shaping to maximize the achievable information rate of coded modulation (CM) with hard decision decoding. The proposed scheme using binary staircase codes outperforms its uniform CM counterpart by more than 1.3 dB for 64-QAM and 5 bits/symbol

Effect of Post Construction Alloy Type (NPG and Ni-Cr) and Cement Type on Fracture Resistance of Endodontically Treated and Restored Teeth by Cast Post-Core

Objectives It is claimed that non-precious gold (NPG) alloys with modulus of elasticity (MOE) very close to dentin’s MOE can enhance the fracture resistance of endodontically treated teeth. Since limited studies have been conducted on these alloys, in this study, we tried to investigate the effect of cast alloys with MOE close to dentin and also the use of resin and zinc phosphate cement on the fracture resistance of endodontically treated teeth. Methods Forty mandibular single canal premolar teeth were assessed after post space endodontic treatment and preparation. The samples were randomly divided into four groups: Group A: Ni-Cr alloy + zinc phosphate cement, group B: Ni-Cr alloy + resin cement (Panavia® F2), group C: NPG alloy + zinc phosphate cement, and group D: NPG alloy + resin cement (Panavia® F2). The force needed for fracture and the fracture pattern of each tooth were recorded. The Shapiro-Wilk test was used to examine the normality of data distribution, Levene’s test was used to examine the equality of variances, and Fisher’s test was used to examine the equality of qualitative variables in the groups. Results A statistically significant difference was observed between the two post-core construction alloys (P<0.0001) and also between the two types of cement used (P<0.001). However, the interaction between alloy and cement type was insignificant (P=0.144). NPG alloy and Panavia® F2 cement showed better results than the other groups. Conclusion The NPG alloy + Panavia® F2 cement technique is preferred in reconstructing endodontically treated teeth

The Difference between Offline and Online Ties in Twitter

Social network sites (SNSs) not only strengthens an existing offline relationship, but also facilitates the formation of a new online relationship. As a result, there coexist the online ties between offline friends and online ties between two users who do not have any offline interactions and connection in SNSs. We investigate the nature of offline ties and its roles on tweet diffusion. We observe some interesting findings: (1) people can spread more efficiently (with fewer hops) their tweet on their offline friends’ local network; (2) offline ties play an essential intermediary role in facilitating pairwise tweet dissemination on each other’s local network; (3) As either in-degree centrality of a network or the number of community clusters increases, the information flow efficiency and edge-between centrality increase

Energy-Efficient Soft-Assisted Product Decoders

We implement a 1-Tb/s 0.63-pJ/bit soft-assisted product decoder in a 28-nm technology. The decoder uses one bit of soft information to improve its net coding gain by 0.2 dB, reaching 10.3-10.4 dB, which is similar to that of more complex hard-decision staircase decoders