What are typical coding gains for modern codes?

At BER=10^-6, rate 1/2: Convolutional (K=7, Viterbi hard): 5.0 dB. Convolutional (K=7, Viterbi soft): 7.0 dB. Turbo code (K=4): 9.5 dB. LDPC (n=64800, DVB-S2): 10.0 dB. Polar (CA-SCL, L=8): 9.8 dB. The Shannon limit for rate 1/2 is 10.3 dB coding gain. Modern codes achieve within 0.3-1.0 dB of the theoretical maximum. Soft-decision decoding provides 2-3 dB more gain than hard-decision.

No. Coding gain comes at costs: (1) Bandwidth expansion: a rate 1/2 code doubles the required bandwidth, which may not be available. (2) Latency: the decoder adds processing delay (microseconds for convolutional, milliseconds for long LDPC). (3) Complexity: turbo and LDPC decoders require significant silicon area and power. (4) Error floor: some codes (turbo, LDPC) have an error floor where BER plateaus at very high Eb/No due to low-weight codewords. The net system benefit must account for all these factors.

Signal Processing

Coding Gain

Q: How is coding gain calculated?

Coding gain = (Eb/No)_uncoded - (Eb/No)_coded at a specified BER. For BPSK, uncoded BER=10^-6 requires Eb/No=10.5 dB. A rate 1/2 convolutional code (K=7, Viterbi) achieves BER=10^-6 at Eb/No=5.0 dB. The coding gain is 10.5 - 5.0 = 5.5 dB. This 5.5 dB gain means the transmitter can reduce power by 5.5 dB or the link can tolerate 5.5 dB more path loss, directly extending range or enabling smaller antennas.

The reduction in required Eb/No to achieve a target BER when using forward error correction compared to uncoded transmission. Coding gain directly translates to reduced transmit power, extended link range, or smaller antenna requirements. Modern LDPC and turbo codes achieve coding gains of 9 to 10 dB at rate 1/2, operating within 0.3 to 1.0 dB of the Shannon limit.

Category: Signal Processing

Unit: dB

Typical range: 3 to 10 dB

Understanding Coding Gain

Without FEC, a BPSK signal needs Eb/No = 10.5 dB to achieve BER = 10⁻⁶. With a rate-1/2 turbo code, the same BER is achieved at Eb/No = 1.0 dB. The 9.5 dB difference is the coding gain. In a satellite link budget, this 9.5 dB translates to either 9.5 dB less transmit power (89% power reduction), 9.5 dB more path loss tolerance (3× range extension for free-space), or a combination of both.

Coding gain is not free: the rate-1/2 code doubles the required bandwidth, and the decoder adds latency and power consumption. The system designer trades bandwidth and complexity for SNR performance. In bandwidth-limited channels, higher code rates (3/4, 5/6) provide less gain but preserve spectral efficiency.

Coding Gain Calculation

Definition:
G_coding = (Eb/No)_uncoded − (Eb/No)_coded at target BER

BPSK uncoded reference:
BER = 10⁻³: Eb/No = 6.8 dB
BER = 10⁻⁶: Eb/No = 10.5 dB

Shannon limit (rate 1/2):
Eb/No_min = 0.19 dB → max coding gain = 10.3 dB

Modern LDPC at rate 1/2 achieves Eb/No = 0.5 dB at BER=10⁻⁶ → coding gain = 10.0 dB.

Coding Gains by FEC Family

Code	Rate	Eb/No @ BER=10⁻⁶	Coding Gain	Gap to Shannon
Uncoded BPSK	1	10.5 dB	0 dB (reference)	N/A
Convolutional (K=7, hard)	1/2	5.5 dB	5.0 dB	5.3 dB
Convolutional (K=7, soft)	1/2	3.5 dB	7.0 dB	3.3 dB
Turbo (K=4)	1/2	1.0 dB	9.5 dB	0.8 dB
LDPC (DVB-S2)	1/2	0.5 dB	10.0 dB	0.3 dB
Polar (CA-SCL L=8)	1/2	0.7 dB	9.8 dB	0.5 dB

Common Questions

Frequently Asked Questions

How is coding gain calculated?

G = (Eb/No)_uncoded − (Eb/No)_coded at the same BER. BPSK at BER=10⁻⁶: uncoded needs 10.5 dB. Rate-1/2 convolutional (Viterbi soft): 3.5 dB. Gain = 7.0 dB. This means 7 dB less transmit power or 2.2× more range.

What are typical gains for modern codes?

At rate 1/2, BER=10⁻⁶: Convolutional 5-7 dB, Turbo 9.5 dB, LDPC 10.0 dB, Polar 9.8 dB. Shannon limit is 10.3 dB. Modern codes are within 0.3-1.0 dB of the theoretical maximum.

Is coding gain free?

No. Costs include: bandwidth expansion (rate 1/2 doubles BW), decoder latency (μs to ms), silicon complexity and power, and error floors at very high Eb/No for some codes (turbo, LDPC).

Related Terms

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