Structure, Optimization, and Realization of FFSK Trellis Codes

Document Type

Article

Publication Date

1-1-1988

Abstract

The structure of combinations of (l, k) binary trellis encoders and fast frequency-shift keying (FFSK) modulation is studied. As a result of the study, a new method for the optimization of these combinations is proposed. The objective is to maximize the free Euclidean distance of the FFSK codes for a given rate k/l and a given number of states in the combined code trellis, i.e., for a given complexity in the corresponding Viterbi decoder. Minimal and nonminimal realizations that produce these codes are considered. It is concluded that, regardless of the particular realization, the best combinations can always be obtained by using a so-called matched convolutional code. Optimum FFSK codes of rates 1 /2 and 2/3 for up to 64 and 32 states, respectively, are reported. These codes are optimum in that the free distance has been maximized and the number of bit errors in the adversaries in the Euclidean distance spectrum has been minimized. It is shown that the best matched encoders for FFSK modulation are also matched and best for any FFSK-type scheme, where the pulse shape is required to satisfy Nyquist#x2019;s third criterion. An interesting result is that about 50 percent of all catastrophic convolutional encoders, matched to FFSK, produce noncatastrophic combinations. © 1988 IEEE

Identifier

0024035527 (Scopus)

Publication Title

IEEE Transactions on Information Theory

External Full Text Location

https://doi.org/10.1109/18.9773

e-ISSN

15579654

ISSN

00189448

First Page

730

Last Page

751

Issue

4

Volume

34

Fund Ref

Natural Sciences and Engineering Research Council of Canada

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