Topic
Chernoff bound
About: Chernoff bound is a research topic. Over the lifetime, 600 publications have been published within this topic receiving 15585 citations. The topic is also known as: Chernoff's inequality & Chernoff inequality.
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Book•
1 Jan 1995TL;DR: Generating Pseudorandom Signals (Pseudonoise) from PseudOrandom Sequences by Modulation and Demodulation of Spread Spectrum Signals in Multipath and Multiple Access Interference.
Abstract: 1. Introduction. Definition and Purpose. Basic Limitations of the Conventional Approach. Spread Spectrum Principles. Organization of the Book. 2. Random and Pseudorandom Signal Generation. Purpose. Pseudorandom Sequences. Maximal Length Linear Shift Register Sequences. Randomness Properties of MLSR Sequences. Conclusion. Generating Pseudorandom Signals (Pseudonoise) from Pseudorandom Sequences. First- and Second-Order Statistics of Demodulator Output in Multiple Access Interference. Statistics for QPSK Modulation by Pseudorandom Sequences. Examples. Bound for Bandlimited Spectrum. Error Probability for BPSK or QPSK with Constant Signals in Additive Gaussian Noise and Interference. Appendix 2A: Optimum Receiver Filter for Bandlimited Spectrum. 3. Synchronization of Pseudorandom Signals. Purpose. Acquisition of Pseudorandom Signal Timing. Hypothesis Testing for BPSK Spreading. Hypothesis Testing for QPSK Spreading. Effect of Frequency Error. Additional Degradation When N is Much Less Than One Period. Detection and False Alarm Probabilities. Fixed Signals in Gaussian Noise (L=1). Fixed Signals in Gaussian Noise with Postdetection Integration (L>1). Rayleigh Fading Signals (L>/=1). The Search Procedure and Acquisition Time. Single-Pass Serial Search (Simplified). Single-Pass Serial Search (Complete). Multiple Dwell Serial Search. Time Tracking of Pseudorandom Signals. Early-Late Gate Measurement Statistics. Time Tracking Loop. Carrier Synchronization. Appendix 3A: Likelihood Functions and Probability Expressions. Bayes and Neyman-Pearson Hypothesis Testing. Coherent Reception in Additive White Gaussian Noise. Noncoherent Reception in AWGN for Unfaded Signals. Noncoherent Reception of Multiple Independent Observations of Unfaded Signals in AWGN. Noncoherent Reception of Rayleigh-Faded Signals in AWGN. 4. Modulation and Demodulation of Spread Spectrum Signals in Multipath and Multiple Access Interference. Purpose. Chernoff and Battacharyya Bounds. Bounds for Gaussian Noise Channel. Chernoff Bound for Time-Synchronous Multiple Access Interference with BPSK Spreading. Chernoff Bound for Time-Synchronous Multiple Access Interference with QPSK Spreading. Improving the Chernoff Bound by a Factor of 2. Multipath Propagation: Signal Structure and Exploitation. Pilot-Aided Coherent Multipath Demodulation. Chernoff Bounds on Error Probability for Coherent Demodulation with Known Path Parameters. Rayleigh and Rician Fading Multipath Components. Noncoherent Reception. Quasi-optimum Noncoherent Multipath Reception for M-ary Orthogonal Modulation. Performance Bounds. Search Performance for Noncoherent Orthogonal M-ary Demodulators. Power Measurement and Control for Noncoherent Orthogonal M-ary Demodulators. Power Control Loop Performance. Power Control Implications. Appendix 4A: Chernoff Bound with Imperfect Parameter Estimates. 5. Coding and Interleaving. Purpose. Interleaving to Achieve Diversity. Forward Error Control Coding - Another Means to Exploit Redundancy. Convolutional Code Structure. Maximum Likelihood Decoder - Viterbi Algorithm. Generalization of the Preceding Example. Convolutional Code Performance Evaluation. Error Probability for Tailed-off Block. Bit Error Probability. Generalizations of Error Probability Computation. Catastrophic Codes. Generalization to Arbitrary Memoryless Channels - Coherent and Noncoherent. Error Bounds for Binary-Input, Output-Symmetric Channels with Integer Metrics. A Near-Optimal Class of Codes for Coherent Spread Spectrum Multiple Access. Implementation. Decoder Implementation. Generating Function and Performance. Performance Comparison and Applicability. Orthogonal Convolutional Codes for Noncoherent Demodulation of Rayleigh Fading Signals. Implementation. Performance for L-Path Rayleigh Fading. Conclusions and Caveats. Appendix 5A: Improved Bounds for Symmetric Memoryless Channels and the AWGN Channel. Appendix 5B: Upper Bound on Free Distance of Rate 1/n Convolutional Codes. 6. Capacity, Coverage, and Control of Spread Spectrum Multiple Access Networks. General. Reverse Link Power Control. Multiple Cell Pilot Tracking and Soft Handoff. Other-Cell Interference. Propagation Model. Single-Cell Reception - Hard Handoff. Soft Handoff Reception by the Better of the Two Nearest Cells. Soft Handoff Reception by the Best of Multiple Cells. Cell Coverage Issues with Hard and Soft Handoff. Hard Handoff. Soft Handoff. Erlang Capacity of Reverse Links. Erlang Capacity for Conventional Assigned-Slot Multiple Access. Spread Spectrum Multiple Access Outage - Single Cell and Perfect Power Control. Outage with Multiple-Cell Interference. Outage with Imperfect Power Control. An Approximate Explicit Formula for Capacity with Imperfect Power Control. Designing for Minimum Transmitted Power. Capacity Requirements for Initial Accesses. Erlang Capacity of Forward Links. Forward Link Power Allocation. Soft Handoff Impact on Forward Link. Orthogonal Signals for Same-Cell Users. Interference Reduction with Multisectored and Distributed Antennas. Interference Cancellation. Epilogue. References and Bibliography. Index.
3,184 citations
TL;DR: This paper presents new probability inequalities for sums of independent, random, self-adjoint matrices and provides noncommutative generalizations of the classical bounds associated with the names Azuma, Bennett, Bernstein, Chernoff, Hoeffding, and McDiarmid.
Abstract: This paper presents new probability inequalities for sums of independent, random, self-adjoint matrices. These results place simple and easily verifiable hypotheses on the summands, and they deliver strong conclusions about the large-deviation behavior of the maximum eigenvalue of the sum. Tail bounds for the norm of a sum of random rectangular matrices follow as an immediate corollary. The proof techniques also yield some information about matrix-valued martingales.
In other words, this paper provides noncommutative generalizations of the classical bounds associated with the names Azuma, Bennett, Bernstein, Chernoff, Hoeffding, and McDiarmid. The matrix inequalities promise the same diversity of application, ease of use, and strength of conclusion that have made the scalar inequalities so valuable.
2,073 citations
TL;DR: The problem of discriminating two different quantum states in the setting of asymptotically many copies is considered, and the minimal probability of error is determined, leading to the identification of the quantum Chernoff bound, thereby solving a long-standing open problem.
Abstract: We consider the problem of discriminating two different quantum states in the setting of asymptotically many copies, and determine the minimal probability of error. This leads to the identification of the quantum Chernoff bound, thereby solving a long-standing open problem. The bound reduces to the classical Chernoff bound when the quantum states under consideration commute. The quantum Chernoff bound is the natural symmetric distance measure between quantum states because of its clear operational meaning and because it does not seem to share some of the undesirable features of other distance measures.
653 citations
TL;DR: In this article, the authors give elementary derivations of the various inequalities collectively known as Chernoff bounds, which are strong upper bounds on the probability of obtaining very few or very many heads in series of independent coin tossings.
593 citations
TL;DR: Relationships between the probability of error, the equivocation, and the Chernoff bound are examined for the two-hypothesis decision problem and the results are extended to the case of any finite number of hypotheses.
Abstract: Relationships between the probability of error, the equivocation, and the Chernoff bound are examined for the two-hypothesis decision problem. The effect of rejections on these bounds is derived. Finally, the results are extended to the case of any finite number of hypotheses.
385 citations
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| Year | Papers |
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| 2025 | 6 |
| 2024 | 3 |
| 2023 | 9 |
| 2022 | 27 |
| 2021 | 21 |
| 2020 | 18 |