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Expanding the Viterbi Algorithm

The Inner Loop: Viterbi Butterflies

Viterbi Decoder Implementation

3-5

We now explain the routine line by line. Begin by moving the address of the

precomputed branch metric table to the r2 address register. In our final, combined

routine, this is unnecessary because the desired value already exists in r2, but we include

it as a comment here to make it clear that this value is needed. Branch metric creation

will be discussed in Section 4.2.

Next, we update the address register that points to the states used to update. The

memory that stores the path metrics is divided into two parts. In this routine, r5 points to

the old path metrics, used to update the new ones. Address register r4 points to the new

states, those being updated. For each new decoder input, we swap the memory used to

store the updated path metrics with the memory pointing to the old path metrics. To do

this, we initialize address registers r4 and r5 to be modulo registers, with a modulus of

twice the number of states. Address incrementing for the butterfly is so designed that at

the end of the loop, r4 and r5 have automatically swapped pointer values. Thus, no

instructions need be dedicated to swapping the memory.

The path metrics are stored in X memory. Collocated with them in Y memory are the

paths. By paths, we mean a word that contains the bit decisions describing the recreated

encoder input data that would produce that path in the decoder. How we get these will

become clear below as we go through this code. By collocating the path metrics with

their respective paths, we can get both by doing long memory moves. The next two

moves load the first branch metric, and the first (state 00000) path metric/path pair.

Now we are ready for the loop. It is necessary to update every state, and we update

states in pairs. Hence, the number of loop passes is equal to the number of states divided

by 2. In our example, this is the value of NoOfAcsButt (i.e., 16).

Because we have polynomials with taps at both ends of the encoder, we can use one

branch metric, and add and subtract to update our states. We begin by subtracting the

branch, loading the second path metric/path pair at the same time.

Next, we add the branch metric to the path metric we just fetched. Note that for both the

subtract and add of the metric, the path metrics in A1 and B1 are affected, but because

we are not performing a long word add, the paths in A0 and B0 are not.

To compute an updated metric, choose the largest result of the subtract/add operations.

The MAX instruction puts the updated result in B. Note that all of A is transferred if A1

is the survivor path, which means that B0 holds the path bits that represent the survivor

path. This instruction also reloads the first path metric/path pair for use in updating the

lower state later in the loop.

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