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Algorithmic Extensions

Allowing More General Branch Metrics

Viterbi Decoder Implementation

4-7

For this example, we are using the same code as in Section 3 to make the unnormalized

branch metrics symmetrical. For easy storage in memory, we want to generate metric

pairs. Each pair should have the values needed for the upper and lower branch metric

value needed for the butterfly. For this example, the branch metric for encoder output 00

will be paired with the branch metric value for 11 and the value for 01 paired with the

value for 10. All branch metrics will have the previous path metric for state 0 subtracted

from them. This means that after the Viterbi butterfly update, each path metric value

will have been normalized. It can be shown that this limits the worst case path metric

values to be no more than 12 times the maximum branch metric value (for this code

example).

The branch metric macro begins by reading in the last path metric for state 0. It then

negates that value in accumulator a and reads the decoder input into register y. The data

in y is assumed to be in the form y1:y0 mapped to real:imaginary data input. Next, the

scaling factor -16 is placed in register x1.

The mac instruction finds a partial branch metric by multiplying the real data by the

scaling factor and adding the result to the negated path metric value in a. We also save

the negated path metric value to b for later use.

Next, we move the real decoder input from y1 to x0. The next mac instruction multiplies

imaginary input by the scaling factor and adds it to a. The accumulator a now has the

normalized branch metric for encoder 00 outputs. At the same time, the partial branch

metric that was in a is saved in y1 for later use.

move

x,l:(r2)+

;store 11 in location 0.

move

ab,l:(r2)+

;store 01 in location 1

move

ba,l:(r2)+

;store 10 in location 2

move

y,l:(r2)+

;store 00 in location 3

move

y,l:(r2)+

;store 00 in location 4

move

ba,l:(r2)+

;store 10 in location 5

move

ab,l:(r2)+

;store 01 in location 6

move

x,l:(r2)+

;store 11 in location 7

move

ba,l:(r2)+

;store 10 in location 8

move

y,l:(r2)+

;store 00 in location 9

move

x,l:(r2)+

;store 11 in location 10

move

ab,l:(r2)+

;store 01 in location 11

move

ab,l:(r2)+

;store 01 in location 12

move

x,l:(r2)+

;store 11 in location 13

move

y,l:(r2)+

;store 00 in location 14

move

ba,l:(r2)+

;store 10 in location 15 r2-> BRX

endm

Example 4-2

Modified Branch Metric Generation Code (Continued)

Freescale Semiconductor, Inc.

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