Trellis source code design as an optimization problem

The design of time-invariant trellis codes for stationary ergodic discrete-time sources is cast as an unconstrained, nonlinear optimization problem, where the objective function and its derivatives are evaluated by simulation. Using classical real analysis and the ergodic theorem, convergence of the...

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Bibliographic Details
Published in:IEEE transactions on information theory 1988-09, Vol.34 (5), p.1226-1241
Main Authors: Freeman, G.H., Blake, I.F., Mark, J.W.
Format: Article
Language:English
Subjects:
Algorithm design and analysis
Applied sciences
Coding, codes
Convergence
Convolutional codes
Design optimization
Encoding
Exact sciences and technology
Information, signal and communications theory
Laplace equations
Nonlinear distortion
Quantization
Signal and communications theory
Speech coding
Telecommunications and information theory
Viterbi algorithm
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Summary:The design of time-invariant trellis codes for stationary ergodic discrete-time sources is cast as an unconstrained, nonlinear optimization problem, where the objective function and its derivatives are evaluated by simulation. Using classical real analysis and the ergodic theorem, convergence of the sample encoding distortion and its partial derivatives (with respect to the code quantization levels) to their ensemble average values is investigated. It is found that in the common code design situation, the expected per-symbol distortion and its first derivatives are available and piecewise continuous, but second-derivative information is unreliable. This indicates that efficient optimization should be performed using a nonderivative or first-derivative method that does not compute approximate second derivatives to determine search directions.< >
ISSN:0018-9448
1557-9654
DOI:10.1109/18.21250