TY - JOUR

T1 - Bounds on Maximum Throughput for Digital Communications with Finite-Precision and Amplitude Constraints

AU - Honig, M. L.

AU - Steiglitz, Kenneth

N1 - Funding Information:
Manuscript received July 7, 1988; revised April 7, 1989. This work was presented in part at the 1988 International Conference on Acoustics, Speech, and Signal Processing, New York, NY, April 11-14, 1988. K. Steiglitz was supported in part by the NSF Grant MIP-8912100, and ARO-Durham Contract DAAL03-89-K-0074, M. L. Honig is with Bell Communications Research, 445 South St., Room MRE 2L-343, Morristown, NJ 07960-1910. K. Steiglitz is with the Department of Computer Science, Princeton, NJ 08544. B. Gopinath is with the Department of Electrical Engineering, Rut-gers University, Piscataway, NJ 08855. S. P. Boyd is with the Information Systems Laboratory, Department of Electrical Engineering. Stanford University, Stanford, CA 94305. IEEE Log Number 8933981.

PY - 1990/5

Y1 - 1990/5

N2 - The problem of finding the maximum achievable data rate over a linear time-invariant channel is considered under constraints different from those typically assumed. The limiting factor is taken to be the accuracy with which the receiver can measure the channel output. More precisely, we consider the following problem. Given a channel with known impulse response h(t), a transmitter with an output amplitude constraint, and a receiver that can distinguish between two signals only if they are separated in amplitude at some time f0 by at least some small positive constant d, what is the maximum number of messages, Nmax, that can be transmitted in a given time interval [0, T]? Lower bounds on Nmaxcan be easily computed by constructing a particular set of inputs to the channel. Our main result is an upper bound on Nmaxfor arbitrary h(t). The upper bound depends on the spread of h(t), which is the maximum range of values the channel output may take at some time f0 > 0 given that the output takes on a particular value a at time t = 0. For a particular h(t), computing the spread in discrete-time is equivalent to solving a linear program with bounded variables and one equality constraint. Solutions to linear programs in this class can be obtained very fast using, for example, a linear-time algorithm due to Witzgall. Numerical results are shown for different impulse responses, including two simulated telephone subscriber loop impulse responses. Assuming that the receiver resolution d is small, the upper bound is typically two to four times the lower bound for the cases examined.

AB - The problem of finding the maximum achievable data rate over a linear time-invariant channel is considered under constraints different from those typically assumed. The limiting factor is taken to be the accuracy with which the receiver can measure the channel output. More precisely, we consider the following problem. Given a channel with known impulse response h(t), a transmitter with an output amplitude constraint, and a receiver that can distinguish between two signals only if they are separated in amplitude at some time f0 by at least some small positive constant d, what is the maximum number of messages, Nmax, that can be transmitted in a given time interval [0, T]? Lower bounds on Nmaxcan be easily computed by constructing a particular set of inputs to the channel. Our main result is an upper bound on Nmaxfor arbitrary h(t). The upper bound depends on the spread of h(t), which is the maximum range of values the channel output may take at some time f0 > 0 given that the output takes on a particular value a at time t = 0. For a particular h(t), computing the spread in discrete-time is equivalent to solving a linear program with bounded variables and one equality constraint. Solutions to linear programs in this class can be obtained very fast using, for example, a linear-time algorithm due to Witzgall. Numerical results are shown for different impulse responses, including two simulated telephone subscriber loop impulse responses. Assuming that the receiver resolution d is small, the upper bound is typically two to four times the lower bound for the cases examined.

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U2 - 10.1109/18.54875

DO - 10.1109/18.54875

M3 - Article

AN - SCOPUS:0025432705

SN - 0018-9448

VL - 36

SP - 472

EP - 484

JO - IEEE Transactions on Information Theory

JF - IEEE Transactions on Information Theory

IS - 3

ER -