2. section (Continued) 6 Call Layer 3 Processing


Hash Functions and Randomization



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2.6.7 Hash Functions and Randomization

2.6.7.1 Hash Function


Certain procedures require a uniform distribution of mobile stations among N resources. The following function returns an integer, using as arguments the mobile station’s IMSI, the number of resources N, and a modifier DECORR. The modifier serves to decorrelate the values obtained for the various applications from the same mobile station.

HASH_KEY shall be equal to the 32 least significant bits of IMSI_O_S1 + 224  IMSI_O_S2).

Define:

• Word L to be bits 0-15 of HASH_KEY



• Word H to be bits 16-31 of HASH_KEY

where bit 0 is the least significant bit of HASH_KEY.

For determining CDMA Channel Number, Paging Channel Number, Quick Paging Channel Number, and Paging Slot Number, the hash value is computed as follows:17

R = N ((40503  (L  H  DECORR)) mod 216 ) / 216

For determining a mobile station’s assigned paging indicator bit positions, the hash value is computed as follows:

R1 = N ((40503  (L  H  DECORR1)) mod 216)/216

and

R2 =  (1 - R1)/(N+4) (N+4)/2 +R1)/(N+4) ((N+4)/2 – 4)) ((40503  (L  H  DECORR2)) mod 216)/216+ N + 4 + R1)/(N+4) ((N+4)/2) for Quick Paging Channel data rate of 4800 bps, or



R2 =  (1 -  R1)/(N+8) (N+8)/2 + R1)/(N+8) ((N+8)/2 – 4) ) ((40503  (L  H  DECORR2)) mod 216)/216+ N + 8 + R1)/(N+8) ((N+8)/2) for Quick Paging Channel data rate of 9600bps.

The mobile station shall choose the range N and the modifiers DECORR, DECORR1, and DECORR2 according to the application as shown in Table 2.6.7.1-1. In the table, HASH_KEY [0...11] denotes the 12 least significant bits of HASH_KEY.


Table 2.6.7.1-1. Hash Function Modifier

Application

N

DECORR

Return
Value


CDMA Channel Number

Number of channels in last CDMA Channel List Message (up to 10)

0

R + 1

Paging Channel Number

PAGE_CHANs from System Parameters Message (up to 7)

2 HASH_KEY [0…11]

R + 1

Quick Paging Channel Number

NUM_QPCHs from Extended System Parameters Message (up to 3)

2 HASH_KEY [0…11]

R + 1

Paging Slot Number

2048

6 HASH_KEY[0…11]

R

Paging Indicator Positions

376 (for 9600 bps), 188 (for 4800 bps)

DECORR1 = t /64 mod 216,

DECORR2 = t /64 + 1 mod 216,

where t is the System Time in frames.


R1 and R2



2.6.7.2 Pseudorandom Number Generator


Where pseudorandom numbers are needed, a linear congruential generator shall be used. The mobile station shall implement the linear congruential generator defined by:

zn = a  zn - 1 mod m

where a = 75 = 16807 and m = 231 - 1 = 2147483647. zn is the output of the generator.18

During the Mobile Station Initialization State, the mobile station shall seed its generator with

z0 = (ESN RANDOM_TIME) mod m

where RANDOM_TIME shall be the least-significant 32-bits of SYS_TIMEs stored from the Sync Channel Message. If the initial value so produced is found to be zero, it shall be replaced with one. The mobile station shall compute a new zn for each subsequent use.

The mobile station shall use the value un = zn / m for those applications that require a binary fraction un, 0 < un < 1.

The mobile station shall use the value kn = N  zn / m for those applications that require a small integer kn, 0  kn  N - 1.


2.6.8 CODE_CHAN_LISTs Maintenance


The CODE_CHAN_LISTs is a descriptive structure used to manage the Forward Fundamental Code Channel and Forward Supplemental Code Channels, if any, associated with the mobile station’s Active Set. Associated with each member of the mobile station’s Active Set, there is an ordered array of code channels. The first entry of the ordered array specifies the Forward Fundamental Code Channel associated with the pilot and the subsequent entries, if any, specify the Forward Supplemental Code Channels associated with the pilot. The CODE_CHAN_LISTs is the collection of ordered arrays of code channels for each member of the mobile station’s Active Set. The ith entry in every array (of code channels associated with a member of the Active Set) corresponds to the ith code channel.

The mobile station shall maintain the CODE_CHAN_LISTsas follows:

• When the mobile station is first assigned a Forward Fundamental Code Channel, it shall initialize the CODE_CHAN_LISTs to contain the Forward Fundamental Code Channel for each member of the Active Set.

• When the mobile station processes the Extended Handoff Direction Message, the mobile station shall update the CODE_CHAN_LISTs as follows:



     For each pilot listed in the Extended Handoff Direction Message which does not have a corresponding code channel in the CODE_CHAN_LISTs, the mobile station shall add the code channel, CODE_CHAN, of that pilot to the CODE_CHAN_LISTs, as the Forward Fundamental Code Channel for the pilot,

     The mobile station shall delete all information in the CODE_CHAN_LISTs associated with a pilot that is not included in the Extended Handoff Direction Message.



• When the mobile station processes the General Handoff Direction Message, the mobile station shall update the CODE_CHAN_LISTs to contain the Forward Fundamental Code Channel associated with each pilot included in the General Handoff Direction Message. The first code channel occurrence associated with each pilot included in the General Handoff Direction Message corresponds to the Forward Fundamental Code Channel. The mobile station shall do the following:

     If FOR_SUP_CONFIGr is included and FOR_SUP_CONFIGr is equal to ‘10’ or ‘11’, the mobile station shall perform the following actions:

+ For each pilot listed in the General Handoff Direction Message, the mobile station shall set the Forward Supplemental Code Channels (associated with the pilot) in the CODE_CHAN_LISTs to the Forward Supplemental Code Channels specified in the General Handoff Direction Message.

+ The mobile station shall delete all information in the CODE_CHAN_LISTs associated with a pilot that is not included in the General Handoff Direction Message.



     If FOR_SUP_CONFIGr is equal to ‘00’ or ‘01’ or if FOR_SUP_CONFIGr is not included in the General Handoff Direction Message, the mobile station shall not update Supplemental Code Channels associated with the pilots included in the General Handoff Direction Message. The mobile station shall perform the following actions:

+ For each pilot listed in the General Handoff Direction Message which does not have a corresponding code channel in the CODE_CHAN_LISTs, the mobile station shall add the code channel, CODE_CHAN, of that pilot to the CODE_CHAN_LISTs, as the Forward Fundamental Code Channel for the pilot.

+ The mobile station shall delete all information in the CODE_CHAN_LISTs associated with a pilot that is not included in the General Handoff Direction Message.

• When the mobile station processes the Supplemental Channel Assignment Message it shall follow the following rules:


     If FOR_SUP_CONFIGr is equal to ‘10’ or ‘11’, the mobile station shall update the Forward Supplemental Code Channels for each pilot in the Active Set.

     If the pilot is not listed in the Supplemental Channel Assignment Message, the mobile station shall delete all occurrences of Forward Supplemental Code Channels associated with the pilot from the Code Channel List.

     If a pilot is listed in the Supplemental Channel Assignment Message, then the mobile station shall set the Forward Supplemental Code Channels (associated with the pilot) in the CODE_CHAN_LISTs to the Forward Supplemental Code Channels specified in the Supplemental Channel Assignment Message.

     If FOR_SUP_CONFIGr is equal to ‘00’ or ‘01’, the mobile station shall not update Supplemental Code Channels associated with the pilots included in the Supplemental Channel Assignment Message.




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