15.01.2013 Views

U. Glaeser

U. Glaeser

U. Glaeser

SHOW MORE
SHOW LESS

You also want an ePaper? Increase the reach of your titles

YUMPU automatically turns print PDFs into web optimized ePapers that Google loves.

FIGURE 42.51 MIPS requirement of several speech coders.<br />

FIGURE 42.52 Viterbi trellis diagram and one butterfly.<br />

is the Viterbi algorithm [4]. It is a dynamic programming technique as it tries to emulate the encoder’s<br />

behavior in creating the transmitted bit sequence. By comparing to the received bit sequence, the<br />

algorithm determines the difference between each possible path through the encoder and the received<br />

bit sequence. The decoder outputs the bit sequence that has the smallest deviation, called the minimum<br />

distance, compared to the received bit sequence.<br />

Most practical convolutional encoders are rate 1/n, meaning that one input bit generates n coded<br />

output bits. A convolutional encoder of constraint length K can be represented by a finite state machine<br />

(FSM) with K − 1 memory bits. The FSM has 2 K−1 possible states, also called trellis states. If the input<br />

is binary, two next states are possible starting from the current state and the input bit. The task of the<br />

Viterbi algorithm is to reconstruct the most likely sequence of state transitions based on the received bit<br />

sequence. This approach is called the “most likelihood sequence estimation.” These state transistions are<br />

represented by a trellis diagram. The kernel of the trellis diagram is the Viterbi butterfly as shown in<br />

Fig. 42.52(b).<br />

Next Generation Applications<br />

Current generation DSP processors are shaped by 2G cellular standards, the main purpose of which is<br />

voice communication. 3G cellular standards will introduce new features: increased focus on data communication,<br />

e-mail, web browsing, banking, navigation, and so on.<br />

2G standards can support short messages, such as the popular SMS messages in the GSM standard,<br />

but are limited to about 10 to 15 kbits/s. In the 2.5G cellular standards, provisions are made to support<br />

higher data rates. By combining GSM time slots, generalized packet radio services (GPRS) can support<br />

up to 115 kbits/s. But the 3G standards are being developed specifically for data services. Wideband<br />

CDMA (WCDMA) will support up to 2 Mbits/s in office environments, lowered to 144 kbits/s for high<br />

mobile situations [6,13].<br />

The increased focus on data services has large consequences for the channel codec design. The traditional<br />

Viterbi decoder does not provide a low enough bit error rate to support data services. Therefore, turbo<br />

© 2002 by CRC Press LLC<br />

[MIPS]<br />

20<br />

15<br />

10<br />

Number of<br />

Operations<br />

5<br />

1<br />

0<br />

PSI-CELP<br />

11.2 kbps<br />

VSELP<br />

13 kbps<br />

VSELP<br />

10 20<br />

RPE-LTP<br />

(a) 000<br />

000<br />

000<br />

(b)<br />

000<br />

11<br />

001<br />

010<br />

011<br />

100<br />

101<br />

110<br />

111<br />

001<br />

010<br />

011<br />

100<br />

101<br />

110<br />

111<br />

11<br />

001<br />

010<br />

011<br />

100<br />

101<br />

110<br />

111<br />

01<br />

001<br />

010<br />

011<br />

100<br />

101<br />

110<br />

111<br />

[kbps]<br />

i<br />

i+s/2<br />

Bit rate<br />

+a<br />

-a<br />

-a<br />

+a<br />

2i<br />

2i+1

Hooray! Your file is uploaded and ready to be published.

Saved successfully!

Ooh no, something went wrong!