Information Technology Reference

In-Depth Information

∞

=

N

=

p

[

n

]

×

n

N

n

1

The number of packets that arrive with error at the sink node can be defined for the

packets without ARQ as the product of the total number of transmitted packets
n
pac
and the

probability that the packet arrives with error at the sink node:

n

=

(

−

P

)

×

n

error

narq

pac

Considering perfect error detection of the CRC code and infinite retransmissions, none of

the ARQ packets is received with errors and thus
n
error
= 0:

n

=

(

−

P

)

×

n

=

0

error

arq

pac

The reliability
R
is given by the percentage of the sent packets being delivered correctly

to the sink node and it may be evaluated as:

R

=

[(

n

−

n

)

/

n

]

pac

error

pac

Since no specific hardware is being used, the energy consumption in the transmission and

reception of the packets is expressed only in normalized terms. While the energies spent in

coding and decoding processes were not considered in [11], [12] and [13], in [10] their effect

on energy efficiency were shown to be negligible compared to the energy consumed in the

transmission of additional parity bits. Thus, only the parity bits of the error control schemes

are considered.

The same model of [7] is considered, where the energy consumed per bit is constant and

the reception of a determined number of bits consumes approximately 75 per cent of the

energy spent to transmit the same number of bits. The minimum energy consumed
E
min
for
H

hops is evaluated for a packet without error control:

(

)

E

=

H

×

n

×

n

+

n

×

0

.

75

min

pac

aux

1

aux

1

where
n
aux1
is the total number of bits of the AUX1 packet. The total energy consumed
E
in a

sensor network for a packet without ARQ and without CRC corresponds to the total number

of bits transmitted and received, where each transmitted bit consumes 1 unit of energy and

each received bit consumes 0.75 units of energy:

(

)

E

=

H

×

n

×

n

+

n

×

0

.

75

pac

bits

bits

where
n
bits
is the total number of bits of a packet, including the access code, header and

payload.

On the oth
er
hand, for the packets with ARQ and CRC and average number of

retransmissions
N
, the energy
E
is: