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Algorithmic Extensions

Introduction

Viterbi Decoder Implementation

4-3

4.1

INTRODUCTION

This section shows how to adjust the code of Section 3 to include several enhancements.

Generalized branch metrics are allowed, as well as optimizing the code to reduce the

computations when data occurs in blocks.

The code in this section introduces several modifications to the code discussed in

Section 3

. Section 4.2 modifies the handling of branch metrics to allow nonsymmetrical

branch metrics. Section 4.3 and Section 4.4 develop two additional macros useful if the

data is blocked and the encoder is periodically forced through a known state. We put all

of these routines together to produce a modified Viterbi algorithm decoder that has

autonormalized path metrics and efficient coding for blocked data. Note that a complete

listing of this code appears in Appendix B.

4.2

ALLOWING MORE GENERAL BRANCH METRICS

The code introduced so far is efficient for algorithms that have special branch metrics. In

particular, the branch metrics are assumed to be inverses of each other and flipped

between state pairs. Although this is true for many popular codes in use today, it is not

necessarily the case. If a polynomial set is specified where one of the encoding

polynomials does not have a tap at one end, the branch metrics lose some of their

symmetry. A simple example is the polynomial set (1,1+D), whose trellis appears in

Figure 4-1

Polynomial (1,1+D) Trellis

Note that the input branches to State 0 are not complements of each other! We might

accommodate this with a fractional branch offset to make branch 00 and branch 01

negatives, but note that the offset for the lower state would have to be different. Another

approach is to compute separate branch offsets for the upper and lower state updates.

This requires a different version of the branch metric generation as well as the butterfly

loop. We consider modified code for each of these functions in the examples that follow.

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