✅ Step-by-Step Plan to Simulate Viterbi Decoding

1. Define a convolutional encoder • Set constraint length K • Define generator polynomials (e.g., [7, 5] in octal for rate 1/2)

2. Generate random input bits • Binary input stream of a given length

3. Encode the bits • Use the convolutional encoder to create a codeword

4. Add noise (optional for BER test) • Pass the encoded stream through an AWGN channel

5. Viterbi decoder • Implement the decoder using a trellis structure • Perform hard-decision or soft-decision decoding

6. Evaluate • Compare decoded bits vs original input • Calculate Bit Error Rate (BER)

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✅ Why Soft-Decision Decoding?

Hard-decision decoding turns the received signal into bits before decoding — potentially throwing away valuable information (e.g., how confident we are in the bit being 0 or 1).

Soft-decision decoding uses the actual received values (e.g., +0.9, -1.2, etc.) to compute path metrics more accurately, based on Euclidean distance rather than Hamming distance.

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🧠 Step-by-Step Plan 1. Leave the encoder and noise simulation unchanged (We’ll still use add_awgn_noise() to generate noisy BPSK values.) 2. Update the Viterbi decoder to use Euclidean distance instead of bit mismatches.

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