Correction:Low-Resolution Precoding for Multi-Antenna Downlink Channels and OFDM(Entropy, (2022), 24, (504), 10.3390/e24040504)

1. Error in Figure In the original publication [1], there was a mistake in Figure 1 as published. The labels of the output signals x1[t] . . . xN[t] should appear at the output of the power amplifier as transmit waveforms. The corrected version of Figure 1 appears below(Figure Presented.). 2. Text Correction There was an error in the original publication. “Blind detector” is incorrect and should be replaced throughout with “data aided detector”. 1. A correction has been made to Abstract: “The information rates are computed for pilot-aided channel estimation and dataaided channel estimation.” 2. A correction has been made to 1. Introduction, 1.2. Discrete Signaling and OFDM, Paragraph Number 1: “For this purpose, we consider two types of channel estimation at the receivers: pilot-aided channel estimation via pilot-aided transmission (PAT) and data-aided channel estimation.“ 3. A correction has been made to 1. Introduction, 1.3. Contributions and Organization, Bullet Point Number 4: “We develop an auxiliary channel model to compute achievable rates for pilot-aided and data-aided channel estimation. The models let one compare modulations, precoders, channels, and receivers;”4. A correction has been made to 4. Performance Metrics, 4.1. Achievable Rates, Paragraph Number 2: “We study the GMI of two non-coherent systems: classic PAT and data-aided channel estimation. For both systems, we apply memoryless signaling with the product distribution” 5. A correction has been made to 4. Performance Metrics, 4.1. Achievable Rates, Paragraph Number 5: “For the data-aided detector we replace Sp with S in (20).” 6. A correction has been made to 4. Performance Metrics, 4.1. Achievable Rates, Paragraph Number 6, Bullet Point 3: “For the data-aided detector, in (21) we replace Sp with the set of all index pairs (`,m), and we replace Sp with S;” 7. A correction has been made to 4. Performance Metrics, 4.1. Achievable Rates, Paragraph Number 5, Bullet Point 4: “For the data-aided detector we set Sp = Æ in (22);” 8. A correction has been made to 4. Performance Metrics, 4.2. Discussion, Paragraph Number 1: “Third, as S grows, the channel estimate of the data-aided detector becomes more accurate and the performance approaches that of a coherent receiver. Related theory for PAT and large S is developed in [49]. However, the PAT rate is generally smaller than for a data-aided detector because the PAT channel estimate is less accurate and because PAT does not use all symbols for data.” 9. A correction has been made to 4. Performance Metrics, 4.2. Discussion, Paragraph Number 2: “We remark that blind channel estimation can approach the performance of data-aided receivers for large S. Blind channel estimation algorithms can, e.g., be based on high-order statistics and iterative channel estimation and decoding.” 10. A correction has been made to 5. Numerical Results, Paragraph Number 2: “The average GMIs for Systems A–C were computed using S = 256, B = 200, and a data-aided detector. The coded results of System D instead have S = 1584 symbols to fit the block structure determined by the LDPC encoder. For System D we considered both PAT and a data-aided detector.” 11. A correction has been made to 5. Numerical Results, Paragraph Number 7: “The solid curves are for data-aided channel estimation and the dotted curves show the performance of PAT when the fraction of pilots is Sp/S = 10%.” 12. A correction has been made to 6. Conclusions, Paragraph Number 1: “The performance was analyzed by computing the GMI for two auxiliary channel models: one model for pilot-aided channel estimation and a second model for a data-aided channel estimation.” The authors state that the scientific conclusions are unaffected. This correction was approved by the Academic Editor. The original publication has also been updated.