Viterbi IP Core User Guide

ID 683280
Date 11/06/2017
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3.3.1. Half-Rate Convolutional Codes

A 1/2 rate convolutional code encodes one information bit and leaves the second information bit uncoded.
Figure 8. Half-Rate Convolutional Code With an eight-point signal constellation (e.g. eight-PSK), the two bits select one of the four subsets in the signal constellation. The remaining information bit selects one of the two points within each subset.
Figure 9. Mapping of Coded Bits and Sector Numbers

The specific mapping is not important. You can derive other mappings by permutating subsets in a way that preserves the main property of increased minimum distance among the subsets. However, you can create any other mapping, including symbol mappings for 8-PSK, 16-PSK and others.

If you create another mapping, you must correctly connect the branch metrics created outside the IP core to the input ports and correctly configure the polynomials GA and GB for the trellis generation.

Figure 10. Four-State Trellis The four-state trellis is the trellis for the 1/2 rate convolution encoder with the addition of parallel paths in each transition to accommodate the uncoded bit c2. The decoder uses the coded bits (c1, c0) to select one of the four subsets that contain two signal points each It uses the uncoded bit to select one of the two signal points within each subset.