Two-Dimensions Alphabetical-Alphabetical Matrix (2DAAM) Numbering


Two-Dimensions Alphabetical-Alphabetical Matrix (2DAAM) Numbering
for Telephone Numbering Plan Systems

More Addresses, Less Number of Digits!
Decimal National Numbering Plan… Goodbye!
Mag. Hasan Meslmani

Abstract- In this paper, a new mechanism for Numbering Plan system of Geographical and Non-geographical for both Public Switched Telephone Network (PSTN) and Public Land Mobile Network (PLMN) is proposed using Two-Dimensions Alphabetical-Alphabetical Numbering (2DAAN), taking into account the increasing demands for numbering capacity for both subscribers and the services in order to meet growth of subscribers numbers and telephone services, such as Free Services or Value-Added Services. This research suggests a new mechanism for numbering which is different from the conventional methods for numbering plans according to recommendations of International Telecommunication Union (ITU) using Pre-Initial Access Isolation Principle (PIASP) and presenting the telephone number as an address for using the whole Possibilities range of Generated Addresses (PGA) for the usage elements. Therefore, this research aims to reduce the digits in telephone number for both fixed and mobile telephones, renumbering the national call code or Local Area Code (LAC) within a certain country, renumbering the Country Code (CC) for each country according to ISO 3166 Alpha-2 Code list, standardization the Length of National Number, and standardization the National Numbering Plan (NNP) in each country.

I. INTRODUCTION
Two-Dimensions Alphabetical-Alphabetical Matrix (2DAAM) numbering
This technique aims to create a huge ranges of addresses for numbering plan by means of using less number of digits taking into account designation of sufficient capacity for geographic areas and non geographic services to meet growth of telephone services, designation of numbering capacity for the future introduction of new services and designation of spare capacity in the form of codes and number ranges that are not associated with any known services and therefore potentially suitable for unforeseen expansion or the introduction of brand new services.
The new mechanism depends on two main stages. The first one assumes enlargement the current numbering range by replacement its decimal elements with bigger range consists of the Latin characters elements which it fortunately already used in the current telephone keypad to execute some secondary functions. The second stage assumes using enlargement principle ones more by dropping these elements on coordinates axis by creating two dimensions mathematical model of Possibilities Theory to obtain on a big base which have the ability to generate huge range of addresses.
It is the right time to redesign a new keypad which contains buttons presenting the Latin Alphabetical characters as a first function to support this technique, [1].
But this requires unfortunately partly or totally opposition some recommendations of the ITU on the international public telecommunication numbering plan such as E.123, E.163, E.164 and E.212, [2].
II. MATHEMATICAL MODEL
A new mathematical model supporting the new mechanism of numbering plan for producing much more addresses sufficient to identify the huge numbers of subscribers has been developed. The general possibilities form of the Mathematical Model for the total sums of Total Generated Addresses (TGA) for a certain range can be written in the following expression (1): [1]

(1)

By choosing the Decimal Number range as a selected range, the previous expression can be re-written as: (2)

(2)

By applying this model on Two Dimensions Matrix (2D Matrix), The general form of Mathematical Model for the possibility of the produced numbers or addresses resulting from a certain range is shown in expression (3)

(3)

Now, by applying this model on Two Dimensions Matrix (2D Matrix), both rows and colons will be the 26th Latin alphabet characters resulting (26*26) Matrix and can be named 2D Alphabetical- Alphabetical Matrix. The components of all elements for the whole range of matrix is given in expression (4)

(4)

Classes of Calls
When this study is applied for Calls Traffic according to Class of Calls for one month by random sample method on a set consisting of (100) suscribers belong to Sabil Exchange in Aleppo city, the following results have been obtaind and summerized in Table 1.

Emergency Service International National Mobile Local Call Types
6 5 4 3 2 1 Levels
%5 %5 %10 %15 %35 %40 Percentages

Table 1: Calls classes
As the result of that, six major classification types of calling can be followed when two A and B parties are executing calling. These classifications are:
1 Local Call
2 Mobile Call
3 National Call
4 International Call
5 Service Call
6 Emergency Call

This classification will help the construction of a new hierarchy call address from one side, guiding to blow up the traditional design of the current telephone keypad and finally inspire the practical steps to redesign the button layout in the new keypad to support this hierarchy from other side, as it is illustrated in Fig. 1, [3,6].

Fig. 1: Classes of calls between the called parties (A) and (B) presentation and its percentages value.

Application of Mathematical Model
The general formula of the Mathematical Model for the total sums of Total Generated Addresses (TGA) possibilities for 2D Alphabetical-Alphabetical Matrix range can be shown in expression (4), from that, the following results can be obtained

A. For n= 1 < Emergency & Services Calls Addresses>:

B. For n= 2 :

C. For n= 3 :

D. For n= 4 :

E. For n= 5 < International Calls Addresses>:

From the previous (7), (10), (13), (16) and (19) equations and matrixes, the following Table shows the Total Generated Addresses (TGA) according to the number of digits for the 2D Alphabetical-Alphabetical Matrix (2DAAM) numbering [1].

5digit 4digit 3digit 2digit 1digit n
141,167,095,653,376 208,827,064,576 308,915,776 456,976 676 TGA

Table 2: Shows the Total Generated Addresses (TGA) according to the number of digits in the proposed (2DAAM) numbering.

While, the Total Generated Addresses (TGA) in connection with the number of digits for the Decimal Numbering can be summerized in Table 3 [7], [8].
7digit 6digit 5digit 4digit 3digit 2digit 1digit n
10,000,000 1,000,000 100,000 10,000 1,000 100 10 TGA

Table 3: Shows the Total Generated Addresses (TGA) according to the number of digits in the current decimal numbering.

By applying this proposed model on different ranges, we can obtain of the following different curves which reflex the value of the selected range, as it shown in Fig. 2. Which shows a possibility of the Total generated addresses produced according to the number of digits in the present numbering system in comparison with other systems, which they are arranged from right to left as follows:
1. Decimal numbering system method
2. Mixed numbering system method
3. IPv4 numbering system method
4. 2D Alphabetical- Alphabetical numbering system method

Fig. 2: Possibilities of the Total Generated Addresses (TGA) produced according to the number of digits.

It is be seen obviously, that the upper curve (2D Alphabetical), which expresses of possibilities of producing the Total Generated Addresses using 2D Matrix components P(x) and P(y) for the Latin Alphabets range, will have the highest values in comparison with the other used ranges (Mixed), (IPv4) and (decimal) curves, [9].

III. THE NEW SUGGESTED HIERARCHY LEVELS
In [1] and [10], The Hierarchy Levels Suggestion can be divided into two main sets as follow:
A. Call Type
The First set can be divided into six subsets as follows:
1. Local Call
2. Mobile Call
3. National Call
4. International Call
5. Service Call
6. Emergency Call
B. Subscriber Address
The second set can be divided into five subsets as follows:
1. State: can be represented by ISO 3166-1 Alpha-2 Codes
2. City: can be represented also by Alpha-2 Codes
3. Exchange: can be represented by Alpha-2 Codes
4. Zone/ Cable: can be represented by Alpha-2 Codes
5. Subscriber: can be represented by Alpha-2 Codes

Types of Two Dimensions Alphabetical-Alphabetical Matrix (2DAAM) calls
In [1], Five types of calls using the 2DAAM are defined when the number of selection digits are equals to Subscriber Address mentioned above? (n=5):

1. Emergency & Service Calls
This category of calls includes all kinds of free services
Emergency & Service ? Numbers are identified by an ‘address’ reflex the two initial characters of the service's name following the type of call Emergency sign or the service identifier ‘1’. This number or address is one digit in length.
Example: 1 {service's name}
Example1 (fire): 1 FI
Example2 (police): 1 PO
The size of the numbers block allocated will generate (676) addresses for services.
The service identifier ‘1’ combined with the short remainder of the number is intended to provide numbers that are easily remembered.

2. Very Local Calls
This category of calls includes all calls between two subscribers belong to the same exchange.
Very Local Calls? Numbers are identified by an ‘address’ reflex the two initial characters of the zone's name and subscriber's name, respectively following the type of very local call sign or the service identifier ‘2’. This number or address is two digits in length.
Example: 2 {zone's name} {subscriber's name}
Example: 2 ZH OM
The block numbers allocated size will generate (456,976) addresses for each exchange.

3. Local Calls
This category of calls includes all calls between two subscribers belong to a different exchanges in the same city or region has the same Local Area Code (LAC).
Local Calls? Numbers are identified by an ‘address’ reflex the two initial characters of the exchange's name, zone's name and subscriber's name respectively? following the type of local call sign or the service identifier ‘3’. This number or address is three digits in length.
Example: 3 {exchange's name} {zone's name} {subscriber's name}
Example: 3 SA ZH OM
The block numbers allocated size will generate (308,915,776) addresses for each city or region.

4. National Calls
This category of calls includes all calls between two subscribers belong to a different exchanges in a different cities or regions has the same Country Code (CC).
National Calls? Numbers are identified by an ‘address’ reflex the two initial characters of the city's name, exchange's name, zone's name and subscriber's name following the type of national call sign or the service identifier ‘4’. This number or address is four digits in length.
Example: 4 {city's name} {exchange's name} {zone's name} {subscriber's name}
Example: 4 AL SA ZH OM
The block numbers allocated size will generate (208,827,064,576) addresses for each country.

5. International Calls
This category of calls includes all calls between two subscribers belong to a different exchanges in a different country has a different Country Code (CC).
International Calls? Numbers are identified by an ‘address’ reflex the two initial characters of the country's name according to ISO 3166-1 Alpha-2 Codes Countries Names table, city's name, exchange's name, zone's name and subscriber's name respectively following the type of international call sign or the service identifier ‘5’. This number or address is five digits in length.
Example: 5 {country's name} {city's name} {exchange's name} {zone's name} {subscriber's name}
Example: 5 SY AL SA ZH OM
The block numbers allocated size will generate (141,167,095,653,376) addresses for the world, or let's say (41,765,412,915,200) addresses for (200) countries around the world, [7].

Geographic Information System (GIS)
It can be also noticed that each address such as (SY AL SA ZH OM) carries Geographic Information System (GIS) meanings; the former address can be read as follows:
The subscriber Omar Meslmani (OM) is a Subscriber belongs to ZHra Zone (ZH) which belongs to Sabil Exchange (SA) in Aleppo City (AL) in Syria State (SY), as it shown in Fig. 3. [1-10].

Fig. 3: The suggested display of the new keypad.

This range of addresses has the ability to define (6,425) address to every living person, whereas IPv4 supports 4.3×10*9 (4.3 billion) addresses, roughly 6.5 billion people population today, which is inadequate for giving even one ?address (0.66) to every living person, [11].

IV. REPRESENTATION THE SUBSCRIBER ADDRESS LEVELS
We can present each level of the five subscriber address levels which consists of Alpha-2 Codes?? as mentioned above by only one digit product from cross point of the horizontal component on (x) axis with the vertical component on (y) axis depending on ?2D Matrix concept by special program means.

A. Local Call representation
Let us suppose that the calling party (A) wishes to execute a Local Call with a called party (B) which has the following address (SA ZH OM). Then the Local Call can be represented by three digits as it shown in Fig. 4.

Fig 4: Local call representation.
1st Pair: SA (Cross Point of Horizontal Component S with Vertical Component A)
2nd Pair: ZH (Cross Point of Horizontal Component Z with Vertical Component H)
3rd Pair: OM (Cross Point of Horizontal Component O with Vertical Component M)
Every pair can be represented by one digit according to the expanded Unicode coding method as it shown in Fig. 5. [1].

Fig. 5: Representation of the alphabetical pair.

B. Mobile Call representation
Let us suppose that the calling party (A) wishes to execute a Mobile Call with a called party (B) which has the following address (MT SA ZH OM). Then the Mobile Call can be represented by four digits as it shown in Fig. 6. [1].

Fig. 6: Mobile call representation.
C. National Call representation
Suppose that the calling party (A) wishes to execute a National? Call with another called party (B) which has the following address (DA DM TJ YM). This address will define the subscriber Yousef Meslmani (YM) which is a Subscriber belongs to Tenth Jazeera Zone (TJ) which belongs to Dummar Exchange (DM) from Damascus City (DA) in Syria State (SY). In this case the National Call can be represented by four digits as it shown in Fig. 7. [1]

Fig. 7: National call representation.
D. International Call representation
Let us consider that the calling party (A) wishes to execute an International? Call with another called party (B) which has the following address (SY AL SA ZH OM). Then the International Call can be represented by five digits as it shown in Fig. 8. [1]

Fig. 8: International call representation.
E. Service Call representation
The new mechanism of numbering should be having the ability to support all type of services calls. Let us suppose that the calling party (A) wishes to execute a Service? Call (Follow Me Immediately) with another (B) party which has the following address (JA MR HM). Then the Service Call can be represented by five digits as it shown in Fig. 9. [1,3-5]

Fig. 9: Service call (Follow Me Immediately) representation.

Let us suppose that the calling party (A) wishes to execute a Service? Call (Alarm Call) at seven clock (HH: 07) and thirty minute (MM: 30) for duration nine and ninety days (DD: 99). Then the Service Call can be represented by five digits as it shown in Fig. 10. [1,3-5]

Fig. 10: Service call (Alarm Call) representation.

F. Emergency Call representation
Suppose that the calling party (A) wishes to execute an Emergency Call with a called party B (Fire) which has the following address (FI). Then the Emergency Call can be represented by one digit as it shown in Fig. 11. [1,3-5]

Fig. 11: Emergency call representation.

Extension of the Unicode Coding Method
We suggest to modify the current database of an Unicode coding method? in order to have the ability to identify the additional (676) new characters or symbols of pair AA, AB, …, MA, MB, …, ZA, ZB, …, ZZ, which resulting from the proposed Mathematical Model for the total sums of Total Generated Addresses (TGA) possibilities for 2D Alphabetical- Alphabetical Matrix (2DAAM) range for (n=1). [9]
Therefore, each pair can be represent by one symbol, then assign each one with the new hexadecimal suggested code of the extended Unicode Coding,? for instance RS= 20A8, whereas it represents in the current main version separately as follows R= 0052 and S= 0053 enable us to merge two symbols in one to save more Bytes!.

V. SOME EXAMPLES AND DISCUSSION
Suggested Dialing of the Telephone Addresses
A. Type of Call Selection
The type of call can be determined by means of several ways in the suggested new keypad. For instance, we can create our own default call type to execute the desired selection by means of check mark method as it shown in Fig. 12. [1]

Fig. 12: Setup default call type.
B. Dialing Called Number
The Dialing Called Number can be execute by another methods differ from the traditional method by means of new keypad which has been developed especially for the new mechanism of numbering according to the following flow chart illustrated in Fig. 13 [7, 8].
The Cursor Position? can be already determined by means of the new keypad type of call selection to reserve number of digits suits to the desired call and compares the value with the initial values of the parameters. Then apply two logical loops, the first one (Loop1) determines the segments of each digit, while, the second one (Loop2) determines the number of digits. [1] ?

Fig. 13: Illustrates the flow chart for 2D Alphabetical- Alphabetical Matrix (2DAAM) numbering.
1. National Call Dialing
Figure 14 illustrates stages of data reception of dialing the International Call, where the Parameter Initial Values will be as follows:? ?
- Type of Call = International {Intern}
- Cursor Position {P=5}
- Number of Digits {D=5}

Fig. 14: International call dialing mechanism.

The total length of address for the International Call dialing will be (5) digits long. The receiving data for the first digit (SY) will be received in the position no. (5), the second digit (AL) will be received in the position no. (4), the third digit (SA) will be received in the position no. (3), the forth digit (ZH) will be received in the position no. (2), and finally the fifth digit (OM) will be received in the position no. (1).

2. National Call Dialing
Figure 15 illustrates stages of data reception of dialing the National Call, where the Parameter Initial Values will be as follows:? ?
- Type of Call = National {Nation}
- Cursor Position {P=4}
- Number of Digits {D=4}

Fig. 15: National call dialing mechanism.

The total length of address for the National Call dialing will be (4) digits long. The receiving data for the first digit (AL) will be received in the position no. (4), the second digit (SA) will be received in the position no. (3), the third digit (ZH) will be received in the position no. (2) and the forth digit (OM) will be received in the position no. (1).

3. Local Call Dialing
Figure 16 illustrates stages of data reception of dialing the Local Call, where the Parameter Initial Values will be as follows:? ?
- Type of Call = Local {Local}
- Cursor Position {P=3}
- Number of Digits {D=3}

Fig. 16: Local call dialing mechanism.
The total length of address for the Local Call dialing will be (3) digits long. The receiving data for the first digit (SA) will be received in the position no. (3), the second digit (ZH) will be received in the position no. (2) and the third digit (OM) will be received in the position no. (1).

4. Emergency Call Dialing
Figure 17 illustrates stages of data reception of dialing the Emergency ? Call, where the Parameter Initial Values will be as follows:? ?
- Type of Call = Emergency {Emerg}
- Cursor Position {P=1}
- Number of Digits {D=1}

Fig. 17: Emergency call dialing mechanism.
In this case, the total length of address for the Emergency Call dialing will be as short as (1) digit long and suits this kind of calls which require higher speed in dialing. The receiving data for the first digit (FI) will be received directly in the position no. (1). [1-10].

VI. CONCLUSION
By applying this method of numbering, we can obtain several practice benefits such as:
1. Identification a Constant Length of the Telephone Address
The identification of constant length of the telephone address will be formatted using the new suggested design of keypad which contains ready blocks for data reception according to 5 levels which represent the basic components of any subscriber. [1] The important result of this representation will be create a standard length of the telephone address can be used around the world and offer at the same time more addresses for far future without any changing.
2. Uniform Identification Format of the Equipment Number (EQN)
As a result, the Equipment Number (EQN) of any subscriber [3-5], will identify with the telephone number or address itself.
3. Re-building New Hierarchy of the Telephone Exchange
The proposed structure of next generation of the telephone exchanges focuses on cancellation some current exchange elements structure such as Shelf name and using uniform design of other element such as Blocks and Cables. [10]
The following Table illustrates that the address of local call will reflex partially the basic elements parameters of exchange hierarchy Exchange room, Main Distribution Frame (MDF) and Network for the current hierarchies of exchanges which represent it the current hierarchy of Siemens (EWSD) system for instance comparing with the suggested hierarchy of the new (HASAN) system as it shown in Fig. 18.

Fig. 18: Illustrate the current proposed parameters in the basic elements of exchanges (Exchange Room, MDF Room and Network).

This Table shows the identification of all parameters of the various elements of communication system (Exchange, MDF and Network) according the suggested hierarchy from one side, and identifying this parameters partially with the telephone address according the suggested numbering plan from other side. Also the Table indicates to the unnecessary parameters which refer to by (X) sign and can be omitted in the new Hierarchy. [1,3-5]
It believed, the time to create a standardized Worldwide Numbering Plans (WNP) instead of the traditional National Numbering Plans (NNP) has come which differ from one country to another by means of creating a certain keypad depending on investing of the Two Dimensions Alphabetical-Alphabetical Numbering (2DAAN)? and support a number of applications like cut, copy, pasting or predict text, or at least and as a first step, trying of investing the advanced present new generations of telephone keypads and its applications such as:
BlackBerry which developed by the Canadian company Research In Motion (RIM), which has a built-in QWERTY keyboard. [12]
IPhone which is an internet-connected multimedia smart phone designed and marketed ?by Apple Inc. Since its minimal hardware interface lacks a physical keyboard, the ?multi-touch screen renders a virtual keyboard when necessary. [13]
For text input, we can also implement a virtual keyboard on the touch screen which has ?automatic spell checking and correction, predictive address capabilities for the 5 elements of suggested Hierarchy:
State, City, Exchange, Zone and Subscriber. The keyboard can predict what word the user is ?typing and complete it, and correct for the accidental pressing of keys adjacent to the ?presumed desired key. [14,15]
Furthermore, we can also use the next generation of this technique (WNP) in the future, which will be the Three Dimensions Alphabetical-Alphabetical- Alphabetical Numbering (3DAAN) in the same manner mentioned above which can supports more and more addresses maybe for requirements of very far future or even forever.

REFERENCES
[1] M. S. H. Ali, M. N. Salaho and H. O. Meslmani, “Development a New Numbering Plan of Telephone Communication Systems,” Aleppo University Magazine publications, Engineering Science Series, vol. 63, Aleppo, Syria, 2008.
[2] “ITU-T Recommendation E.164,” Assigned country codes, Geneva, Swiss, 2005.
[3] “Digital electronic switching system EWSD,” Siemens training center for communication networks, Munich, Germany, 2000.
[4] “Operating system documents of local exchange EWSD,” for Syrian Telecommunication Establishment (STE) project, Siemens company, Munich, Germany, Sept. 2001.
[5] “Operating system documents of Ericsson exchange,” for Syrian Telecommunication Establishment (STE) project, Ericsson company, Stockholm, Sweden, Feb. 2003.
[6] “Syrian Estimation Group Results,” Geography and population, Damascus, Syria, 2007.
[7] “Public Switched Telephone Network (PSTN) ,” European Telecommunication Standards Institute (ETSI), Paris, France, 1997.
[8] L. W. Couh, “Digital and Analog Communications System,” Macmillan publishing company, 2nd Ed., New York, USA, 1997.
[9] L. HUGHES, “Data Communications,” Mc Graw-Hill, 2nd Ed., New York, USA, 1998.
[10] M. S. H. Ali, M. N. Salaho and H. O. Meslmani, “Development a New Hierarchy of Exchanges,” Aleppo University, Magazine publications, Engineering Science Series, vol. 64, Aleppo, Syria, 2008.
[11] “The World Fact Book,” Geography and population rank order publications, New York, USA, July 2007.
[12] Research In Motion Reports Fourth Quarter And Year-End Results For Fiscal
2006. http://www.blackberry.com/??
[13] Apple Inc. (2008-06-09). Apple Introduces the New iPhone 3G. Press release. ?http://www.apple.com/pr/library/2008/06/09iphone.html. Retrieved on 2008-??06-09.
???[14] ?"The most advanced mobile OS. Now even more advanced.". Scott Forstall's ?presentation. Apple. 2009-03-17. ?
[15] Cohen, Peter, "Cut and paste, MMS highlight iPhone 3.0 ?improvements". Macworld. 2009-03-17 ?http://www.macworld.com/article/139438/2009/03/iphone30user.html. ?Retrieved on 2009-04-01. ?

Hasan Omar Meslmani was born in Aleppo, Syria, on June 4, 1964. He received B.Sc. (with honors) degrees in electrical and electronic engineering in 1988 and M.Sc. degrees in communication engineering in 2004, from Aleppo University, Aleppo, Syria. He joined the Syrian Telecommunication Establishment (STE), Aleppo Directorate in 1988, as a technician engineer, from 1988 to 1990, he was operating and maintaining engineer at Jamilieh Exchange (NEC System NEAX61), from 1991 to 1992, he was an installation Department Head at Jamilieh Exchange, from 1992 to 1993, he was a supervisor engineer at Ensari Exchange, from 1993 to 1994, he was a supervisor engineer at Sabil Exchange, from 1994 to 2007, he was a Head Exchange of Sabil Exchange, from 1998 to 2007, he was a Supervisor for Automatic Billing System for Sabil Exchange in Aleppo,
Successfully completed training course at Siemens Training Center for Communication Networks in Munich, Germany (Siemens System EWSD) in1992, he has been a member of the Telecommunication Development Committee in Syria for 21st century, in Syrian Telecommunication Establishment (STE) in1996,
Successfully completed training course at STE Training Center for Radio Communications at High Institute for Application & Technology Science in Damascus, Syria in1998,

After that, a successfully completed training course at Ericsson Training Center for Communication Networks in Dublin, Ireland (Ericsson System AXE 10) in 2000. He enrolled as Ph.D. student in electronic engineering in Communication Department, Aleppo University in 2006.

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