FEC Coding Gain Calculator

FEC Coding Gain Calculator: Calculate coding gain for Hamming, Reed-Solomon, Convolutional, Turbo, LDPC & Polar codes. Compare BER vs Eb/N0 performance.

📐 FEC Coding Gain Calculator

Compare Forward Error Correction Schemes — ITU-R BS.1111 Compliant

Coding Gain = (Eb/N₀)_uncoded − (Eb/N₀)_coded

⚙️ Configuration

Select FEC Code

Convolutional Rate 1/2

Turbo Rate 1/2

LDPC Rate 1/2

Uncoded BPSK Rate 1

Code Rate (R)

Target BER 10⁻⁵

Constraint Length (K) 7

Turbo Iterations 8

LDPC Block Length 10,000

Convolutional (2,1,7): Constraint length K=7, rate R=1/2. Well-known code with coding gain ~4–5 dB at BER 10⁻⁵. Viterbi decoding provides optimal soft-decision performance.

Coding Gain

0.0

dB improvement

0 dB 10 dB 12 dB

Uncoded BPSK

9.60

Reference

Convolutional

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Turbo Code

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LDPC

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📈 BER vs. Eb/N₀ — Coded vs Uncoded

📐 Code-Specific Formulas & Thresholds

Convolutional Code (2,1,K)

G(D) = [1, 1+D+D²] for K=7

Free distance d_free determines performance. Soft-decision Viterbi decoding. Coding gain ≈ 4.1 dB (K=7, R=1/2) at BER=10⁻⁵.

Turbo Code (Parallel Concatenated)

BER ≈ f(R, N_iter, d_free₁, d_free₂)

Two recursive systematic convolutional encoders + interleaver. Iterative MAP/BCJR decoding approaches Shannon limit. Coding gain ≈ 8.9 dB at BER=10⁻⁵.

LDPC (Quasi-Cyclic)

BER ≈ f(R, N, d_min, column weight)

Sparse parity-check matrix H. Belief propagation decoding. Near-Shannon limit performance. Coding gain ≈ 9.1 dB at BER=10⁻⁵.

Uncoded BPSK (Reference)

BER = ½ · erfc(√(Eb/N₀))

Baseline performance without any coding. Requires Eb/N₀ = 9.6 dB for BER = 10⁻⁵. Serves as reference for computing coding gain.

FEC Coding Gain Calculator