On the performance of convolutional codes

by Onyszchuk, Ivan M.

Abstract (Summary)
This thesis contains error bounds, algorithms, and techniques for evaluating the performance of convolutional codes on the Additive White Gaussian Noise (AWGN) channel. Convolutional encoders are analyzed using simple binary operations in order to determine the longest possible "zero-run" output and if "catastrophic error propagation" may occur. Methods and algorithms are presented for computing the weight enumerator and other generating functions, associated with convolutional codes, which are used to upper-bound maximum-likelihood (i.e., Viterbi) decoder error rates on memoryless channels. In particular, the complete path enumerator T(D, L, I) is obtained for the memory 6, rate 1/2, NASA standard code. A new, direct technique yields the corresponding bit-error generating function. These procedures may be used to count paths between nodes in a finite directed graph or to calculate transfer functions in circuits and networks modelled by signal flow graphs. A modified Viterbi decoding algorithm is used to obtain numbers for error bound computations. New bounds and approximations for maximum-likelihood convolutional decoder first-event, bit, and symbol error rates are derived, the latter one for concatenated coding system analysis. Berlekamp's tangential union bound for maximum-likelihood, block decoder word error probability on the AWGN channel is adapted for convolutional codes. Approximations to bit and symbol error rates are obtained that remain within 0.2 dB of simulation results at low signal-to-noise ratios, where many convolutional codes operate but the standard bounds are useless. An upper bound on the loss caused by truncating survivors in a Viterbi decoder leads to estimates of minimum practical truncation lengths. Lastly, the power loss due to quantizing received (demodulated) symbols from the AWGN channel is studied. Effective schemes are described for uniform channel symbol quantization, branch metric calculations, and path metric renormalization in Viterbi decoders.
Bibliographical Information:

Advisor:Edward C. Posner; Robert J. McEliece; P. P. Vaidyanathan

School:California Institute of Technology

School Location:USA - California

Source Type:Master's Thesis

Keywords:electrical engineering


Date of Publication:05/23/1990

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