Designing a pipelined parallel Viterbi decoder using VHDL for a specified constraint length, code rate, and set of generator polynomials involves multiple steps, from defining the architecture to implementing the VHDL code. Below, I'll guide you through the high-level design and provide an outline of the VHDL code to accomplish this. The Viterbi algorithm is used extensively in digital communications to decode convolutionally encoded data.

### High-Level Design:

1. **Specifications**:
- **Constraint Length (K)**: 7
- **Code Rate (R)**: 1/6
- **Generator Polynomials (octal format)**: 175, 171, 151, 133, 127, 117.

2. **Input/Output**:
- **Input Width**: 64-bit
- **Output Width**: 64-bit

3. **Architecture**:
- The decoder will be pipelined to enhance throughput. This means dividing the decoding process into multiple stages, each stage handling a part of the decoding process.
- **Trellis Diagram**: Based on the constraint length, the trellis will have \(2^{K-1} = 64\) states.

4. **Path Metrics and Traceback**:
- **Path Metric Calculation**: Calculate using the Hamming distance between the received bits and the expected bits for each transition.
- **Traceback**: Store decisions in a buffer and trace back from the most likely end state to decode the sequence.

5. **Branch Metrics Calculation**:
- Convert the generator polynomials to binary and use them to calculate the expected output bits for each state transition.

### VHDL Code Outline:

Here is a simplified VHDL module outline to give you a starting point. Note that detailed implementations of each component like branch metric calculation, path metric updates, and the traceback logic are complex and require thorough testing.

```vhdl
library IEEE;
use IEEE.STD_LOGIC_1164.ALL;
use IEEE.NUMERIC_STD.ALL;

entity ViterbiDecoder is
Port ( clk : in STD_LOGIC;
reset : in STD_LOGIC;
input_stream : in STD_LOGIC_VECTOR(63 downto 0);
output_stream : out STD_LOGIC_VECTOR(63 downto 0));
end ViterbiDecoder;

architecture Behavioral of ViterbiDecoder is

— Define the generator polynomials
constant gen_poly : array (0 to 5) of std_logic_vector(6 downto 0) := (
"1011111", — 175 octal
"1011001", — 171 octal
"1010101", — 151 octal
"1001101", — 133 octal
"1001111", — 127 octal
"1000111" — 117 octal
);

— Signal declarations
signal branch_metrics : std_logic_vector(5 downto 0);
signal path_metrics : std_logic_vector(255 downto 0); — Adjust based on actual path metric width requirements
signal decoded_bits : std_logic_vector(63 downto 0);

begin

process(clk, reset)
begin
if reset = '1' then
— Initialization logic
elsif rising_edge(clk) then
— Main decoding logic, including path metric update and traceback
end if;
end process;

output_stream <= decoded_bits;

end Behavioral;
```

### Key Considerations:
- **State Encoding**: Each state should be encoded efficiently to simplify the transitions and branch metric calculations.
- **Parallelism**: Implement path metric updates and other calculations in parallel where possible to utilize the 64-bit architecture.
- **Testing**: Thoroughly simulate the decoder with various test vectors to ensure all paths and states are correctly handled.

This outline gives a structural view of a Viterbi decoder in VHDL. Each subcomponent like metric calculations and the traceback mechanism needs to be explicitly designed and tested. The generator polynomials must be converted correctly to guide the creation of expected bit sequences for branch metric calculations. Consider using VHDL testbenches extensively to validate each part of the decoder.