Andrew J. Viterbi

The probability of error in decoding an optimal convolutional code transmitted over a memoryless channel is bounded from above and below as a function of the constraint length of the code. For all but pathological channels the bounds are asymptotically (exponentially) tight for rates above <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R_{0}</tex> , the computational cutoff rate of sequential decoding. As a function of constraint length the performance of optimal convolutional codes is shown to be superior to that of block codes of the same length, the relative improvement increasing with rate. The upper bound is obtained for a specific probabilistic nonsequential decoding algorithm which is shown to be asymptotically optimum for rates above <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R_{0}</tex> and whose performance bears certain similarities to that of sequential decoding algorithms.

It is shown that, particularly for terrestrial cellular telephony, the interference-suppression feature of CDMA (code division multiple access) can result in a many-fold increase in capacity over analog and even over competing digital techniques. A single-cell system, such as a hubbed satellite network, is addressed, and the basic expression for capacity is developed. The corresponding expressions for a multiple-cell system are derived. and the distribution on the number of users supportable per cell is determined. It is concluded that properly augmented and power-controlled multiple-cell CDMA promises a quantum increase in current cellular capacity.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

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.

This classic by two digital communications experts is geared toward students of communications theory and to designers of channels, links, terminals, modems, or networks used to transmit and receive digital messages. 1979 edition.

This tutorial paper begins with an elementary presentation of the fundamental properties and structure of convolutional codes and proceeds with the development of the maximum likelihood decoder. The powerful tool of generating function analysis is demonstrated to yield for arbitrary codes both the distance properties and upper bounds on the bit error probability for communication over any memoryless channel. Previous results on code ensemble average error probabilities are also derived and extended by these techniques. Finally, practical considerations concerning finite decoding memory, metric representation, and synchronization are discussed.