2-D Codes With & Without the Chip-Sync

8/2/2019 2-D Codes With & Without the Chip-Sync

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A NEW FAMILY OF 2-D CODES FOR

FIBRE-OPTIC CDMA SYSTEMS WITH

AND WITHOUT THE CHIP-

SYNCHRONOUS ASSUMPTION

By Yongzhen Chen

A REVIEW OF


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ABSTRACT

Based on 1-D OOCs of cross-correlation value at most two;

Provide larger cardinality for accommodating moresubscribers;

Support heavier code weight for better performance;

Newer chip-asynchronous assumption offers a moreaccurate analysis, while the traditional chip-synchronousassumption gives pessimistic performance;

Under certain conditions, the new 2-D codesoutperform 1 MWOOCs and 2 2-D codes recentlyreported.


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INTRODUCTION

Potential applications:

Supports multi-rate, multimedia services in OCDMAwith different data-rate and QoS requirements:

Assign multiple distinct code matrices to each user,and then the multi-rate transmission of a user isachieved by sending different numbers of distinct codematrices in parallel, as a function of that users data

rate. Supports multi-code keying in OCDMA:

2m distinct code matrices is allocated to each userto represent the transmission of m data bits/symbol.


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INTRODUCTION (CONT)

Advantages of multi-code keying O-CDMA:

The data rate is increased by m times of thebaud;

User code confidentiality is improved becausedata bits zeros are also transmitted in codematrices; eavesdroppers cannot determine thetransmission of bit zeros or ones by simplydetecting the absence or presence of intensity inthe downlink fibre.


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CODE CONSTRUCTION

The new ( , , 1,2) 2-D codes areconstructed by first choosing a (,,1,2)OOC as the time-spreading code.

The wavelength used in each non-zero timeslot of the time-spreading code is arranged inaccordance with the permutation of

wavelength indices, algebraically controlledby synchronous prime sequences.


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CODE MATRICES PERMUTATION

1. Divide the synchronous prime sequencesinto groups of sequences each;

2. Use the first sequence of each group as a

seed to generate other 1 shiftedsequences in the group, resulting a total of

2sequences;

3. For , use only the th elements ineach synchronous prime sequences ofthese groups in the permutations.


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CARDINALITY

Let (,,, ) be the cardinality of 1-D (,,, )OOCs. We have:

,,, OOC

, for odd , for even ,for

< 8. (1)

,,, OOC

, for odd , for even

, (2)

,,, OOC () (3) ,,, OOC= ,,, OOC. (4)


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CARDINALITY (CONT)

From (1)-(4), the (,,1,2) OOCs always have the largestcardinality, resulting the new 2-D codes with the largestcardinality, which is about and /2 times greater than thatof the MWOOCs and the ,,2,1 2-D codes, respectively.


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ERROR PROBABILITY

Chip-Synchronous assumption:

,sy,ha 12

= 1

=0 [0

( )( 1)( 1) ] Chip-Asynchronous assumption:

,asy,ha 12

=

=0 2 1 + 2

+=0

[0,0 (0, ,0)

(0, ,0 ,)

(, ,) 3

3 , 4

4 ]

Where 0,0 1 (0, ,0 , , , ,0 0, ,).


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NEW 2D CODE VS. MWOOC


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NEW 2D CODE VS. PREVIOUS 2D CODE


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ASYNC. VS. SYNC.


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DIFFERENT THRESHOLD UNDER ASYNC.

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2-D Codes With & Without the Chip-Sync