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Series Editors Mario Gerla parallel Aurel Lazar sequence Paul generator Kuhn Hideaki Takagi

Figure 9.6. An SSRG-based minimal PSRG generating the 8-deci-

mated sequences Uj's in (9.2). This PSRG can be used as the PSRG for parallel scrambling the STM-1 or STS-1 signal. Inserting this into (7.45) along with (9.2b) and qim(x) = x7 + X + 1, we obtain the minimal PSRG with the state transition matrix T = A~7 +:1)+1 ' the initial state vector do = So, and the generating vectors

ho= hI = h2 = h3 = h4 = = hs= h7 = hs

[ 1 0 0 0 0 0 0 ]t, [ 0 0 1 0 1 0 0 ]t, [ 0 11 0 1 0 0 ]t, [ 0 11111 0 ]t,

[0100100]t, [ 0 111 0 11 ]t, [ 0 1 0 1 0 0 1]t,

(9.3)

[ 1 0 1 0 1 0 0 ]t.

The circuit diagram for this minimal PSRG is as shown in Fig. 9.6, which becomes an SSRG-based realization. This PSRG can be used as the PSRG in Fig. 9.5(b) for parallel scrambling the STM-1 or STS-1 signal. To get a simpler minimal PSRG, we choose another nonsingular ma-

Byeong Gi Lee

Seok Chang Kim

Scrambling Techniques for Digital Transmission

With 124 Illustrations

Springer-Verlag London Berlin Heidelberg New York Paris Tokyo Hong Kong Barcelona. Budapest

Byeong Gi Lee, BS, ME, PhD Seok Chang Kim, BS, ME, PhD Department of Electronics Engineering, Seoul National University, Seoul 151-742, Korea

Series Editors Mario Gerla Department of Computer Science University of California Los Angeles CA 90024, USA

Paul Kuhn Institute of Communications Switching and Data Technics University of Stuttgart D-70174 Stuttgart, Germany

Aurel Lazar Department of Electrical Engineering and Center for Telecommunications Research Columbia University New York, NY 10027, USA

Hideaki Takagi IBM Japan Ltd Tokyo Research Laboratory 5-19 Sanban-cho Chiyoda-ku, Tokyo 102, Japan

ISBN-13:978-1-4471-3233-2 e-ISBN-13:978-1-4471-3231-8 DOl: 10.1007/978-1-4471-3231-8 British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms of licences issued by the Copyright Licensing Agency. Enquiries concerning reproduction outside those terms should be sent to the publishers. Springer-Verlag London Limited 1994 Softcover reprint of the hardcover 1st edition 1994

II

The publisher makes no representation, express or implied, with regard to the accuracy of the information contained in this book and cannot accept any legal responsibility or liability for any errors or omissions that may be made. Typesetting: Camera ready by authors 69/3830-543210 Printed on acid-free paper

Preface

Scramblers and the constituent shift register generators (SRG) have been used for decades in shaping the digital transmission signals or in generating pseudo-random binary