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Fabian Steiner

Publications and source records attributed to Fabian Steiner.

At least 19 recordsLinked to original sources
arXiv2022

Low-Resolution Precoding for Multi-Antenna Downlink Channels and OFDM

Downlink precoding is considered for multi-path multi-input single-output channels where the base station uses orthogonal frequency-division multiplexing and low-resolution signaling. A quantized coordinate minimization (QCM) algorithm is proposed and its performance is compared to other precoding algorithms including squared infinity-norm relaxation (SQUID), multi-antenna greedy iterative quantization (MAGIQ), and maximum safety margin precoding. MAGIQ and QCM achieve the highest information rates and QCM has the lowest complexity measured in the number of multiplications. The information rates are computed for pilot-aided channel estimation and data-aided channel estimation. Bit error rates for a 5G low-density parity-check code confirm the information-theoretic calculations. Simulations with imperfect channel knowledge at the transmitter show that the performance of QCM and SQUID degrades in a similar fashion as zero-forcing precoding with high resolution quantizers.

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arXiv2020

Probabilistically Shaped 4-PAM for Short-Reach IM/DD Links with a Peak Power Constraint

Probabilistic shaping for intensity modulation and direct detection (IM/DD) links is discussed and a peak power constraint determined by the limited modulation extinction ratio (ER) of optical modulators is introduced. The input distribution of 4-ary unipolar pulse amplitude modulation (PAM) symbols is optimized for short-reach transmission links without optical amplification nor in-line dispersion compensation. The resulting distribution is symmetric around its mean allowing to use probabilistic amplitude shaping (PAS) to generate symbols that are protected by forward error correction (FEC) and that have the optimal input distribution. The numerical analysis is confirmed experimentally for both an additive white Gaussian noise (AWGN) channel and a fiber channel, showing gains in transmission reach and transmission rate, as well as rate adaptability.

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arXiv2019

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.

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arXiv2019

Shaped On-Off Keying Using Polar Codes

The probabilistic shaping scheme from Honda and Yamamoto (2013) for polar codes is used to enable power-efficient signaling for on-off keying (OOK). As OOK has a non-symmetric optimal input distribution, shaping approaches that are based on the concatenation of a distribution matcher followed by systematic encoding do not result in optimal signaling. Instead, these approaches represent a time sharing scheme where only a fraction of the codeword symbols is shaped. The proposed scheme uses a polar code for joint distribution matching and forward error correction which enables asymptotically optimal signaling. Numerical simulations show a gain of 1.8 dB compared to uniform transmission at a spectral efficiency of 0.25 bits/channel use for a blocklength of 65,536 bits.

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arXiv2019

Design of Polar Codes for Parallel Channels with an Average Power Constraint

Polar codes are designed for parallel binary-input additive white Gaussian noise (BiAWGN) channels with an average power constraint. The two main design choices are: the mapping between codeword bits and channels of different quality, and the power allocation under the average power constraint. Information theory suggests to allocate power such that the sum of mutual information (MI) terms is maximized. However, a power allocation specific to polar codes shows significant gains.

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arXiv2019

Efficient Error-Correcting Codes in the Short Blocklength Regime

The design of block codes for short information blocks (e.g., a thousand or less information bits) is an open research problem that is gaining relevance thanks to emerging applications in wireless communication networks. In this paper, we review some of the most promising code constructions targeting the short block regime, and we compare them with both finite-length performance bounds and classical error-correction coding schemes. The work addresses the use of both binary and high-order modulations over the additive white Gaussian noise channel. We will illustrate how to effectively approach the theoretical bounds with various performance versus decoding complexity tradeoffs.

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arXiv2019

Probabilistic Parity Shaping for Linear Codes

Linear layered probabilistic shaping (LLPS) is proposed, an architecture for linear codes to efficiently encode to shaped code words. In the previously proposed probabilistic amplitude shaping (PAS) architecture, a distribution matcher (DM) maps information bits to shaped bits, which are then systematically encoded by appending uniformly distributed parity bits. LLPS extends PAS by probabilistic parity shaping (PPS), which uses a syndrome DM to calculate shaped parity bits. LLPS enables the transmission with any desired distribution using linear codes, furthermore, by LLPS, a given linear code with rate $R_\text{fec}$ can be operated at any rate $R\leq R_\text{fec}$ by changing the distribution. LLPS is used with an LDPC code for dirty paper coding against an interfering BPSK signal, improving the energy efficiency by 0.8 dB.

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arXiv2019

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.

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arXiv2018

Divergence-Optimal Fixed-to-Fixed Length Distribution Matching With Shell Mapping

Distribution matching (DM) transforms independent and Bernoulli(1/2) distributed bits into a sequence of output symbols with a desired distribution. A fixed-to-fixed length, invertible DM architecture based on shell mapping is presented. It is shown that shell mapping for distribution matching (SMDM) is the optimum DM for the informational divergence metric and that finding energy optimal sequences is a special case of divergence minimization. Additionally, it is shown how to find the required shell mapping weight function to approximate arbitrary output distributions. SMDM is combined with probabilistic amplitude shaping (PAS) to operate close to the Shannon limit. SMDM exhibits excellent performance for short blocklengths as required by ultra-reliable low-latency (URLLC) applications. SMDM outperforms constant composition DM (CCDM) by 0.6 dB when used with 64-QAM at a spectral efficiency of 3 bits/channel use and a 5G low-density parity-check code with a short blocklength of 192 bits

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arXiv2018

Construction and Decoding Algorithms for for Polar Codes based on $2\times2$ Non-Binary Kernels

Polar codes based on $2\times2$ non-binary kernels are discussed in this work. The kernel over $\text{GF}(q)$ is selected by maximizing the polarization effect and using Monte-Carlo simulation. Belief propagation (BP) and successive cancellation (SC) based decoding algorithms are extended to non-binary codes. Additionally, a successive cancellation list (SCL) decoding with a pruned tree is proposed. Simulation results show that the proposed decoder performs very close to a conventional SCL decoder with significantly lower complexity.

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arXiv2018

Protograph-Based LDPC Code Design for Ternary Message Passing Decoding

A ternary message passing (TMP) decoding algorithm for low-density parity-check codes is developed. All messages exchanged between variable and check nodes have a ternary alphabet, and the variable nodes exploit soft information from the channel. A density evolution analysis is developed for unstructured and protograph-based ensembles. For unstructured ensembles the stability condition is derived. Optimized ensembles for TMP decoding show asymptotic gains of up to 0.6 dB with respect to ensembles optimized for binary message passing decoding. Finite length simulations of codes from TMP-optimized ensembles show gains of up to 0.5 dB under TMP compared to protograph-based codes designed for unquantized belief propagation decoding.

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arXiv2018

Optimization of Bit Mapping and Quantized Decoding for Off-the-Shelf Protograph LDPC Codes with Application to IEEE 802.3ca

Protograph-based, off-the-shelf low-density parity-check (LDPC) codes are optimized for higher-order modulation and quantized sum-product decoders. As an example, for the recently proposed LDPC code from the upcoming IEEE 802.3ca standard for passive optical networks (PONs), an optimized mapping of the bit channels originating from bit-metric decoding to the protograph variable nodes gains 0.4 dB and 0.3 dB at a bit-error rate of 1e-6 for shaped and uniform signaling, respectively. Furthermore, the clipping value for a quantized sum-product LDPC decoder is optimized via discretized density evolution.

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arXiv2018

Bit-Metric Decoding of Non-Binary LDPC Codes with Probabilistic Amplitude Shaping

A new approach for combining non-binary low-density parity-check (NB-LDPC) codes with higher-order modulation and probabilistic amplitude shaping (PAS) is presented. Instead of symbol-metric decoding (SMD), a bit-metric decoder (BMD) is used so that matching the field order of the non-binary code to the constellation size is not needed, which increases the flexibility of the coding scheme. Information rates, density evolution thresholds and finite-length simulations show that the flexibility comes at no loss of performance if PAS is used.

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arXiv2018

Flexible IR-HARQ Scheme for Polar-Coded Modulation

A flexible incremental redundancy hybrid auto- mated repeat request (IR-HARQ) scheme for polar codes is proposed based on dynamically frozen bits and the quasi-uniform puncturing (QUP) algorithm. The length of each transmission is not restricted to a power of two. It is applicable for the binary input additive white Gaussian noise (biAWGN) channel as well as higher-order modulation. Simulation results show that this scheme has similar performance as directly designed polar codes with QUP and outperforms LTE-turbo and 5G-LDPC codes with IR-HARQ.

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arXiv2018

Approaching Waterfilling Capacity of Parallel Channels by Higher Order Modulation and Probabilistic Amplitude Shaping

Parallel, additive white Gaussian noise (AWGN) channels with an average sum power constraint are considered. It is shown how the waterfilling Shannon capacity can be approached by higher order modulation and probabilistic amplitude shaping (PAS). This is achieved by a new distribution matching approach called product distribution matching (PDM). The asymptotic performance of PDM is analyzed by achievable rates. A heuristic for optimizing the input distribution is proposed, which enables signaling at a target spectral efficiency with a fixed-rate forward error correction (FEC) code, while the optimal power allocation is ensured by mercury-waterfilling and a simple bit-loading strategy. Finite blocklength simulation results with 5G low-density parity-check codes show power savings of around 1 dB compared to a conventional scheme with uniform input distributions.

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