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The growth in the number of low-cost narrow band radios such as Bluetooth low energy (BLE) enabled applications such as asset tracking, human behavior monitoring, and keyless entry. The accurate range estimation is a must in such applications. Phase-based ranging has recently gained momentum due to its high accuracy in multipath environment compared to traditional schemes such as ranging based on received signal strength. The phase-based ranging requires tone exchange on multiple frequencies on a uniformly sampled frequency grid. Such tone exchange may not be possible due to some missing tones, e.g., reserved advertisement channels. Furthermore, the IQ values at a given tone may be distorted by interference. In this paper, we proposed two phase-based ranging schemes which deal with the missing/interfered tones. We compare the performance and complexity of the proposed schemes using simulations, complexity analysis, and measurement setups. In particular, we show that for small number of missing/interfered tones, the proposed system based on employing a trained neural network (NN) performs very close to a reference ranging system where there is no missing/interference tones. Interestingly, this high performance is at the cost of negligible additional computational complexity and up to 60.5 Kbytes of additional required memory compared to the reference system, making it an attractive solution for ranging using hardware-limited radios such as BLE., Comment: Accepted for publication in IEEE Internet of Things Journal

Recently, a metric called energy dispersion index (EDI) was proposed to indicate the nonlinear interference (NLI) induced by correlated symbols during optical transmission. In this paper, we propose a new shaper architecture to decrease the EDI of transmitted symbols and thus, increase the signal-to-noise ratio (SNR). We call this shaper the list-encoding constant-composition distribution matcher (L-CCDM). L-CCDM consists of an additional EDI selecting module, which is compatible with standard probabilistic amplitude shaping (PAS) architecture. Numerical results obtained from a multi-span multi-channel system show that when compared to standard CCDM with 256-ary quadrature amplitude modulation (256QAM), the proposed architecture offers an effective SNR gain of 0.35 dB, an achievable information rate gain of 0.22 bit/4D-symbol, or equivalently an 8% reach extension.

The stationary statistical properties of independent, identically distributed (i.i.d.) input symbols provide insights on the induced nonlinear interference (NLI) during fiber transmission. For example, kurtosis is known to predict the modulation format-dependent NLI. These statistical properties can be used in the design of probabilistic amplitude shaping (PAS), which is a popular scheme that relies on an amplitude shaper for increasing spectral efficiencies of fiber-optic systems. One property of certain shapers used in PAS -- including constant-composition distribution matchers -- that is often overlooked is that a time-dependency between amplitudes is introduced. This dependency results in symbols that are non-i.i.d., which have time-varying statistical properties. Somewhat surprisingly, the effective signal-to-noise ratio (SNR) in PAS has been shown to increase when the shaping blocklength decreases. This blocklength dependency of SNR has been attributed to time-varying statistical properties of the symbol sequences, in particular, to variation of the symbol energies. In this paper, we investigate the temporal energy behavior of symbol sequences, and introduce a new metric called energy dispersion index (EDI). EDI captures the time-varying statistical properties of symbol energies. Numerical results show strong correlations between EDI and effective SNR, with absolute correlation coefficients above 99% for different transmission distances.

Product codes (PCs) and staircase codes (SCCs) are conventionally decoded based on bounded distance decoding (BDD) of the component codes and iterating between row and column decoders. The performance of iterative BDD (iBDD) can be improved using soft-aided (hybrid) algorithms. Among these, iBDD with combined reliability (iBDD-CR) has been recently proposed for PCs, yielding sizeable performance gains at the expense of a minor increase in complexity compared to iBDD. In this paper, we first extend iBDD-CR to SCCs. We then propose two novel decoding algorithms for PCs and SCCs which improve upon iBDD-CR. The new algorithms use an extra decoding attempt based on error and erasure decoding of the component codes. The proposed algorithms require only the exchange of hard messages between component decoders, making them an attractive solution for ultra high-throughput fiber-optic systems. Simulation results show that our algorithms based on two decoding attempts achieve gains of up to $0.88$ dB for both PCs and SCCs. This corresponds to a $33\%$ optical reach enhancement over iBDD with bit-interleaved coded modulation using $256$ quadrature amplitude modulation.

We propose a novel soft-aided iterative decoding algorithm for product codes (PCs). The proposed algorithm, named iterative bounded distance decoding with combined reliability (iBDD-CR), enhances the conventional iterative bounded distance decoding (iBDD) of PCs by exploiting some level of soft information. In particular, iBDD-CR can be seen as a modification of iBDD where the hard decisions of the row and column decoders are made based on a reliability estimate of the BDD outputs. The reliability estimates are derived using extrinsic message passing for generalized low-density-parity check (GLDPC) ensembles, which encompass PCs. We perform a density evolution analysis of iBDD-CR for transmission over the additive white Gaussian noise channel for the GLDPC ensemble. We consider both binary transmission and bit-interleaved coded modulation with quadrature amplitude modulation.We show that iBDD-CR achieves performance gains up to $0.51$ dB compared to iBDD with the same internal decoder data flow. This makes the algorithm an attractive solution for very high-throughput applications such as fiber-optic communications.

Current optical coherent transponders technology is driving data rates towards 1 Tb/s/{\lambda}and beyond. This trend requires both high-performance coded modulation schemes and efficient implementation of the forward-error-correction (FEC) decoder. A possible solution to this problem is combining advanced multidimensional modulation formats with low-complexity hybrid HD/SD FEC decoders. Following this rationale, in this paper we combine two recently introduced coded modulation techniques:the geometrically-shaped 4D-64 polarization ring-switched and the soft-aided bit-marking-scaled reliability decoder. This joint scheme enabled us to experimentally demonstrate the transmission of 11x218 Gbit/s channels over transatlantic distances at 5.2bit/4D-sym. Furthermore, a 30% reach increase is demonstrated over PM-8QAM and conventional HD-FEC decoding for product codes., Comment: This work has been submitted to IEEE Photonics Technology Letters

We use density evolution to optimize the parameters of binary product codes (PCs) decoded based on the recently introduced iterative bounded distance decoding with scaled reliability. We show that binary PCs with component codes of 3-bit error correcting capability provide the best performance-complexity trade-off.

Probabilistic amplitude shaping (PAS) can flexibly vary the spectral efficiency (SE) of fiber-optic systems. In this paper, we demonstrate the application of PAS to bit-wise hard decision decoding (HDD) of product codes (PCs) by finding the necessary conditions to select the PC component codes. We show that PAS with PCs and HDD yields gains up to $2.7$ dB and SE improvement up to approximately $1$ bit/channel use compared to using PCs with uniform signaling and HDD. Furthermore, we employ the recently introduced iterative bounded distance decoding with combined reliability of PCs to improve performance of PAS with PCs and HDD., Comment: Accepted for publication in IEEE Communications Letters

We introduce a novel soft-aided hard-decision decoder for product codes adopting bit marking via updated reliabilities at each decoding iteration. Gains up to 0.8 dB vs. standard iterative bounded distance decoding and up to 0.3 dB vs. our previously proposed bit-marking decoder are demonstrated.

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 Communications

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:1806.10903

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.

We study low-complexity iterative decoding algorithms for product codes. We revisit two algorithms recently proposed by the authors based on bounded distance decoding (BDD) of the component codes that improve the performance of conventional iterative BDD (iBDD). We then propose a novel decoding algorithm that is based on generalized minimum distance decoding of the component codes. The proposed algorithm closes over 50% of the performance gap between iBDD and turbo product decoding (TPD) based on the Chase-Pyndiah algorithm. Moreover, the algorithm only leads to a limited increase in complexity with respect to iBDD and has significantly lower complexity than TPD. The studied algorithms are particularly interesting for high-throughput fiber-optic communications.

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.

We consider probabilistic amplitude shaping (PAS) as a means of increasing the spectral efficiency of fiber-optic communication systems. In contrast to previous works in the literature, we consider probabilistic shaping with hard decision decoding (HDD). In particular, we apply the PAS recently introduced by B\"ocherer \emph{et al.} to a coded modulation (CM) scheme with bit-wise HDD that uses a staircase code as the forward error correction code. We show that the CM scheme with PAS and staircase codes yields significant gains in spectral efficiency with respect to the baseline scheme using a staircase code and a standard constellation with uniformly distributed signal points. Using a single staircase code, the proposed scheme achieves performance within $0.57$--$1.44$ dB of the corresponding achievable information rate for a wide range of spectral efficiencies., Comment: Published in IEEE/OSA Journal of Lightwave Technology, 2017

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, 2017

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.