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Time parallelization, also known as PinT (parallel-in-time), is a new research direction for the development of algorithms used for solving very large-scale evolution problems on highly parallel computing architectures. Despite the fact that interesting theoretical work on PinT appeared as early as 1964, it was not until 2004, when processor clock speeds reached their physical limit, that research in PinT took off. A distinctive characteristic of parallelization in time is that information flow only goes forward in time, meaning that time evolution processes seem necessarily to be sequential. Nevertheless, many algorithms have been developed for PinT computations over the past two decades, and they are often grouped into four basic classes according to how the techniques work and are used: shooting-type methods; waveform relaxation methods based on domain decomposition; multigrid methods in space–time; and direct time parallel methods. However, over the past few years, it has been recognized that highly successful PinT algorithms for parabolic problems struggle when applied to hyperbolic problems. We will therefore focus on this important aspect, first by providing a summary of the fundamental differences between parabolic and hyperbolic problems for time parallelization. We then group PinT algorithms into two basic groups. The first group contains four effective PinT techniques for hyperbolic problems: Schwarz waveform relaxation (SWR) with its relation to tent pitching; parallel integral deferred correction; ParaExp; and ParaDiag. While the methods in the first group also work well for parabolic problems, we then present PinT methods specifically designed for parabolic problems in the second group: Parareal; the parallel full approximation scheme in space–time (PFASST); multigrid reduction in time (MGRiT); and space–time multigrid (STMG). We complement our analysis with numerical illustrations using four time-dependent PDEs: the heat equation; the advection–diffusion equation; Burgers’ equation; and the second-order wave equation.
Channel coding lies at the heart of digital communication and data storage. Fully updated, including a new chapter on polar codes, this detailed introduction describes the core theory of channel coding, decoding algorithms, implementation details, and performance analyses. This new edition includes over 50 new end-of-chapter problems and new figures and worked examples throughout. The authors emphasize the practical approach and present clear information on modern channel codes, including turbo and low-density parity-check (LDPC) codes, detailed coverage of BCH codes, Reed-Solomon codes, convolutional codes, finite geometry codes, product codes as well as polar codes for error correction and detection, providing a one-stop resource for classical and modern coding techniques. Assuming no prior knowledge in the field of channel coding, the opening chapters begin with basic theory to introduce newcomers to the subject. Later chapters then extend to advanced topics such as code ensemble performance analyses and algebraic code design.
One hundred and thirteen mid-lactation cows fed same diets and supplemented with 20 g/d rumen-protected methionine (RPM) for 8 weeks were used to investigate the individual responses of dairy cows to RPM in terms of lactation performance, amino acids (AA) metabolism, and milk metabolites. Among the cows, 10 cows exhibited positive responses (PR) and 10 cows showed limited responses (LR) in energy-corrected milk yield to RPM were used for further analysis. The lactation performance changed from gradual decline to steady increase in PR cows, while kept downward trend in LR cows following RPM supplementation. In PR cows, the AA metabolism was notably enhanced after RPM supplementation, evidenced by increased mammary blood flow (69.4%, P = 0.05), mammary uptake and clearance rate and uptake-to-output ratio (U:O) of essential AA. The improved AA metabolism could be attributed to the enrichment of pyrimidine (P = 0.06) and pyruvate (P = 0.07) metabolism pathways, which may have stimulated mammary cell proliferation and enhanced AA uptake. Additionally, the upregulation of milk biotin (fold change > 2, variable importance projection > 1), known to support milk yield, likely contributed to the PR observed in PR cows. Conversely, in LR cows, RPM supplementation did not improve AA metabolism, decrease was observed in mammary uptake, mammary clearance rate, and U:O of cysteine, potentially due to cysteine being irreversibly converted from methionine. Moreover, the enrichment of central carbon metabolism in cancer pathway (P = 0.06), which also utilize methionine, along with the lysine degradation pathway (P = 0.04), suggests that methionine in the mammary glands may have been diverted toward non-lactational metabolic processes, resulting in absence of PR in LR cows. Our results indicate that the responses to RPM in dairy cows are individualized, with variation in lactation performance likely driven by differential AA metabolism.
Channel coding lies at the heart of digital communication and data storage. Fully updated to include current innovations in the field, including a new chapter on polar codes, this detailed introduction describes the core theory of channel coding, decoding algorithms, implementation details, and performance analyses. This edition includes over 50 new end-of-chapter problems to challenge students and numerous new figures and examples throughout.
The authors emphasize a practical approach and clearly present information on modern channel codes, including polar, turbo, and low-density parity-check (LDPC) codes, as well as detailed coverage of BCH codes, Reed–Solomon codes, convolutional codes, finite geometry codes, and product codes for error correction, providing a one-stop resource for both classical and modern coding techniques.
Assuming no prior knowledge in the field of channel coding, the opening chapters begin with basic theory to introduce newcomers to the subject. Later chapters then begin with classical codes, continue with modern codes, and extend to advanced topics such as code ensemble performance analyses and algebraic LDPC code design.
300 varied and stimulating end-of-chapter problems test and enhance learning, making this an essential resource for students and practitioners alike.
Provides a one-stop resource for both classical and modern coding techniques.
Starts with the basic theory before moving on to advanced topics, making it perfect for newcomers to the field of channel coding.
180 worked examples guide students through the practical application of the theory.
Channel coding lies at the heart of digital communication and data storage. Fully updated to include current innovations in the field, including a new chapter on polar codes, this detailed introduction describes the core theory of channel coding, decoding algorithms, implementation details, and performance analyses. This edition includes over 50 new end-of-chapter problems to challenge students and numerous new figures and examples throughout.
The authors emphasize a practical approach and clearly present information on modern channel codes, including polar, turbo, and low-density parity-check (LDPC) codes, as well as detailed coverage of BCH codes, Reed–Solomon codes, convolutional codes, finite geometry codes, and product codes for error correction, providing a one-stop resource for both classical and modern coding techniques.
Assuming no prior knowledge in the field of channel coding, the opening chapters begin with basic theory to introduce newcomers to the subject. Later chapters then begin with classical codes, continue with modern codes, and extend to advanced topics such as code ensemble performance analyses and algebraic LDPC code design.
300 varied and stimulating end-of-chapter problems test and enhance learning, making this an essential resource for students and practitioners alike.
Provides a one-stop resource for both classical and modern coding techniques.
Starts with the basic theory before moving on to advanced topics, making it perfect for newcomers to the field of channel coding.
180 worked examples guide students through the practical application of the theory.
Channel coding lies at the heart of digital communication and data storage. Fully updated to include current innovations in the field, including a new chapter on polar codes, this detailed introduction describes the core theory of channel coding, decoding algorithms, implementation details, and performance analyses. This edition includes over 50 new end-of-chapter problems to challenge students and numerous new figures and examples throughout.
The authors emphasize a practical approach and clearly present information on modern channel codes, including polar, turbo, and low-density parity-check (LDPC) codes, as well as detailed coverage of BCH codes, Reed–Solomon codes, convolutional codes, finite geometry codes, and product codes for error correction, providing a one-stop resource for both classical and modern coding techniques.
Assuming no prior knowledge in the field of channel coding, the opening chapters begin with basic theory to introduce newcomers to the subject. Later chapters then begin with classical codes, continue with modern codes, and extend to advanced topics such as code ensemble performance analyses and algebraic LDPC code design.
300 varied and stimulating end-of-chapter problems test and enhance learning, making this an essential resource for students and practitioners alike.
Provides a one-stop resource for both classical and modern coding techniques.
Starts with the basic theory before moving on to advanced topics, making it perfect for newcomers to the field of channel coding.
180 worked examples guide students through the practical application of the theory.
Channel coding lies at the heart of digital communication and data storage. Fully updated to include current innovations in the field, including a new chapter on polar codes, this detailed introduction describes the core theory of channel coding, decoding algorithms, implementation details, and performance analyses. This edition includes over 50 new end-of-chapter problems to challenge students and numerous new figures and examples throughout.
The authors emphasize a practical approach and clearly present information on modern channel codes, including polar, turbo, and low-density parity-check (LDPC) codes, as well as detailed coverage of BCH codes, Reed–Solomon codes, convolutional codes, finite geometry codes, and product codes for error correction, providing a one-stop resource for both classical and modern coding techniques.
Assuming no prior knowledge in the field of channel coding, the opening chapters begin with basic theory to introduce newcomers to the subject. Later chapters then begin with classical codes, continue with modern codes, and extend to advanced topics such as code ensemble performance analyses and algebraic LDPC code design.
300 varied and stimulating end-of-chapter problems test and enhance learning, making this an essential resource for students and practitioners alike.
Provides a one-stop resource for both classical and modern coding techniques.
Starts with the basic theory before moving on to advanced topics, making it perfect for newcomers to the field of channel coding.
180 worked examples guide students through the practical application of the theory.
Channel coding lies at the heart of digital communication and data storage. Fully updated to include current innovations in the field, including a new chapter on polar codes, this detailed introduction describes the core theory of channel coding, decoding algorithms, implementation details, and performance analyses. This edition includes over 50 new end-of-chapter problems to challenge students and numerous new figures and examples throughout.
The authors emphasize a practical approach and clearly present information on modern channel codes, including polar, turbo, and low-density parity-check (LDPC) codes, as well as detailed coverage of BCH codes, Reed–Solomon codes, convolutional codes, finite geometry codes, and product codes for error correction, providing a one-stop resource for both classical and modern coding techniques.
Assuming no prior knowledge in the field of channel coding, the opening chapters begin with basic theory to introduce newcomers to the subject. Later chapters then begin with classical codes, continue with modern codes, and extend to advanced topics such as code ensemble performance analyses and algebraic LDPC code design.
300 varied and stimulating end-of-chapter problems test and enhance learning, making this an essential resource for students and practitioners alike.
Provides a one-stop resource for both classical and modern coding techniques.
Starts with the basic theory before moving on to advanced topics, making it perfect for newcomers to the field of channel coding.
180 worked examples guide students through the practical application of the theory.
Channel coding lies at the heart of digital communication and data storage. Fully updated to include current innovations in the field, including a new chapter on polar codes, this detailed introduction describes the core theory of channel coding, decoding algorithms, implementation details, and performance analyses. This edition includes over 50 new end-of-chapter problems to challenge students and numerous new figures and examples throughout.
The authors emphasize a practical approach and clearly present information on modern channel codes, including polar, turbo, and low-density parity-check (LDPC) codes, as well as detailed coverage of BCH codes, Reed–Solomon codes, convolutional codes, finite geometry codes, and product codes for error correction, providing a one-stop resource for both classical and modern coding techniques.
Assuming no prior knowledge in the field of channel coding, the opening chapters begin with basic theory to introduce newcomers to the subject. Later chapters then begin with classical codes, continue with modern codes, and extend to advanced topics such as code ensemble performance analyses and algebraic LDPC code design.
300 varied and stimulating end-of-chapter problems test and enhance learning, making this an essential resource for students and practitioners alike.
Provides a one-stop resource for both classical and modern coding techniques.
Starts with the basic theory before moving on to advanced topics, making it perfect for newcomers to the field of channel coding.
180 worked examples guide students through the practical application of the theory.
Channel coding lies at the heart of digital communication and data storage. Fully updated to include current innovations in the field, including a new chapter on polar codes, this detailed introduction describes the core theory of channel coding, decoding algorithms, implementation details, and performance analyses. This edition includes over 50 new end-of-chapter problems to challenge students and numerous new figures and examples throughout.
The authors emphasize a practical approach and clearly present information on modern channel codes, including polar, turbo, and low-density parity-check (LDPC) codes, as well as detailed coverage of BCH codes, Reed–Solomon codes, convolutional codes, finite geometry codes, and product codes for error correction, providing a one-stop resource for both classical and modern coding techniques.
Assuming no prior knowledge in the field of channel coding, the opening chapters begin with basic theory to introduce newcomers to the subject. Later chapters then begin with classical codes, continue with modern codes, and extend to advanced topics such as code ensemble performance analyses and algebraic LDPC code design.
300 varied and stimulating end-of-chapter problems test and enhance learning, making this an essential resource for students and practitioners alike.
Provides a one-stop resource for both classical and modern coding techniques.
Starts with the basic theory before moving on to advanced topics, making it perfect for newcomers to the field of channel coding.
180 worked examples guide students through the practical application of the theory.
Channel coding lies at the heart of digital communication and data storage. Fully updated to include current innovations in the field, including a new chapter on polar codes, this detailed introduction describes the core theory of channel coding, decoding algorithms, implementation details, and performance analyses. This edition includes over 50 new end-of-chapter problems to challenge students and numerous new figures and examples throughout.
The authors emphasize a practical approach and clearly present information on modern channel codes, including polar, turbo, and low-density parity-check (LDPC) codes, as well as detailed coverage of BCH codes, Reed–Solomon codes, convolutional codes, finite geometry codes, and product codes for error correction, providing a one-stop resource for both classical and modern coding techniques.
Assuming no prior knowledge in the field of channel coding, the opening chapters begin with basic theory to introduce newcomers to the subject. Later chapters then begin with classical codes, continue with modern codes, and extend to advanced topics such as code ensemble performance analyses and algebraic LDPC code design.
300 varied and stimulating end-of-chapter problems test and enhance learning, making this an essential resource for students and practitioners alike.
Provides a one-stop resource for both classical and modern coding techniques.
Starts with the basic theory before moving on to advanced topics, making it perfect for newcomers to the field of channel coding.
180 worked examples guide students through the practical application of the theory.
Channel coding lies at the heart of digital communication and data storage. Fully updated to include current innovations in the field, including a new chapter on polar codes, this detailed introduction describes the core theory of channel coding, decoding algorithms, implementation details, and performance analyses. This edition includes over 50 new end-of-chapter problems to challenge students and numerous new figures and examples throughout.
The authors emphasize a practical approach and clearly present information on modern channel codes, including polar, turbo, and low-density parity-check (LDPC) codes, as well as detailed coverage of BCH codes, Reed–Solomon codes, convolutional codes, finite geometry codes, and product codes for error correction, providing a one-stop resource for both classical and modern coding techniques.
Assuming no prior knowledge in the field of channel coding, the opening chapters begin with basic theory to introduce newcomers to the subject. Later chapters then begin with classical codes, continue with modern codes, and extend to advanced topics such as code ensemble performance analyses and algebraic LDPC code design.
300 varied and stimulating end-of-chapter problems test and enhance learning, making this an essential resource for students and practitioners alike.
Provides a one-stop resource for both classical and modern coding techniques.
Starts with the basic theory before moving on to advanced topics, making it perfect for newcomers to the field of channel coding.
180 worked examples guide students through the practical application of the theory.
Channel coding lies at the heart of digital communication and data storage. Fully updated to include current innovations in the field, including a new chapter on polar codes, this detailed introduction describes the core theory of channel coding, decoding algorithms, implementation details, and performance analyses. This edition includes over 50 new end-of-chapter problems to challenge students and numerous new figures and examples throughout.
The authors emphasize a practical approach and clearly present information on modern channel codes, including polar, turbo, and low-density parity-check (LDPC) codes, as well as detailed coverage of BCH codes, Reed–Solomon codes, convolutional codes, finite geometry codes, and product codes for error correction, providing a one-stop resource for both classical and modern coding techniques.
Assuming no prior knowledge in the field of channel coding, the opening chapters begin with basic theory to introduce newcomers to the subject. Later chapters then begin with classical codes, continue with modern codes, and extend to advanced topics such as code ensemble performance analyses and algebraic LDPC code design.
300 varied and stimulating end-of-chapter problems test and enhance learning, making this an essential resource for students and practitioners alike.
Provides a one-stop resource for both classical and modern coding techniques.
Starts with the basic theory before moving on to advanced topics, making it perfect for newcomers to the field of channel coding.
180 worked examples guide students through the practical application of the theory.
Channel coding lies at the heart of digital communication and data storage. Fully updated to include current innovations in the field, including a new chapter on polar codes, this detailed introduction describes the core theory of channel coding, decoding algorithms, implementation details, and performance analyses. This edition includes over 50 new end-of-chapter problems to challenge students and numerous new figures and examples throughout.
The authors emphasize a practical approach and clearly present information on modern channel codes, including polar, turbo, and low-density parity-check (LDPC) codes, as well as detailed coverage of BCH codes, Reed–Solomon codes, convolutional codes, finite geometry codes, and product codes for error correction, providing a one-stop resource for both classical and modern coding techniques.
Assuming no prior knowledge in the field of channel coding, the opening chapters begin with basic theory to introduce newcomers to the subject. Later chapters then begin with classical codes, continue with modern codes, and extend to advanced topics such as code ensemble performance analyses and algebraic LDPC code design.
300 varied and stimulating end-of-chapter problems test and enhance learning, making this an essential resource for students and practitioners alike.
Provides a one-stop resource for both classical and modern coding techniques.
Starts with the basic theory before moving on to advanced topics, making it perfect for newcomers to the field of channel coding.
180 worked examples guide students through the practical application of the theory.
Channel coding lies at the heart of digital communication and data storage. Fully updated to include current innovations in the field, including a new chapter on polar codes, this detailed introduction describes the core theory of channel coding, decoding algorithms, implementation details, and performance analyses. This edition includes over 50 new end-of-chapter problems to challenge students and numerous new figures and examples throughout.
The authors emphasize a practical approach and clearly present information on modern channel codes, including polar, turbo, and low-density parity-check (LDPC) codes, as well as detailed coverage of BCH codes, Reed–Solomon codes, convolutional codes, finite geometry codes, and product codes for error correction, providing a one-stop resource for both classical and modern coding techniques.
Assuming no prior knowledge in the field of channel coding, the opening chapters begin with basic theory to introduce newcomers to the subject. Later chapters then begin with classical codes, continue with modern codes, and extend to advanced topics such as code ensemble performance analyses and algebraic LDPC code design.
300 varied and stimulating end-of-chapter problems test and enhance learning, making this an essential resource for students and practitioners alike.
Provides a one-stop resource for both classical and modern coding techniques.
Starts with the basic theory before moving on to advanced topics, making it perfect for newcomers to the field of channel coding.
180 worked examples guide students through the practical application of the theory.