Convolutional Code (Viterbi)

Code with memory, decoded using Viterbi algorithm

Real-World Applications

NASA Voyager deep space exploration, GSM voice channel coding, WiFi (802.11a/g/n/ac) internal coding mechanism. The Viterbi decoding algorithm is even the foundation of HMM models in today voice recognition and NLP.

Experiment Steps

Trellis Diagram: Observe path metric accumulation
Coding Gain: SNR savings compared to uncoded

Simulation Experiment

Convolutional Code Viterbi Decoding Demo

Constraint Length K: 3Num States: 4Generator Polynomials: [0o7, 0o5]Eb/N0: 1.0 dBChannel Error Rate: 13.09%

Input:

Encoded:

Received:

Decoded:

BER: 0.0%

Trellis Diagram: Numbers on nodes are cumulative Hamming distance (path metric). Purple path is the optimal decoding path found by Viterbi algorithm. Solid=input 0, Dashed=input 1.

Effect of Constraint Length K: Larger K means more states (2^(K-1)), stronger error correction, but exponentially higher complexity.

Parameters(Real-time)

Code Rate0.5

Constraint Length K3

Eb/N01 dB

← Cyclic Redundancy Check

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