How is code combining implemented in 5G NR?

5G NR uses LDPC coding with redundancy versions (RV) to implement code combining. The LDPC encoder produces all coded bits at the mother code rate (1/3 for BG1), and the rate matching module selects which bits to transmit based on the redundancy version number (RV0, RV1, RV2, RV3). Each RV starts reading from a different position in the circular buffer of encoded bits: RV0 starts at the beginning of the systematic bits, RV2 starts at approximately 1/3 of the buffer, RV1 at approximately 2/3, and RV3 near the end. The first transmission typically uses RV0 (which includes all systematic bits plus some parity), and retransmissions use RV2, RV3, or RV1, each providing mostly new parity bits. The receiver stores all received soft bits in a soft buffer indexed by their position in the circular buffer, and after each retransmission, the LDPC decoder operates on the combined buffer with more filled positions and therefore lower effective code rate. The soft buffer size per HARQ process is limited by UE memory, defined by the UE category.

What is the throughput gain of code combining over chase combining?

The throughput advantage of code combining depends on the operating SNR and the initial code rate. At low SNR where the initial transmission rarely succeeds and multiple retransmissions are common, code combining provides 20 to 40% higher throughput than chase combining because each retransmission adds new coding information rather than just diversity. At high SNR where the initial transmission usually succeeds and retransmissions are rare, the advantage shrinks because few packets need retransmission. Quantitatively, in a Rayleigh fading channel at average SNR of 5 dB with initial rate 3/4: chase combining achieves approximately 1.2 bps/Hz average throughput while code combining achieves approximately 1.6 bps/Hz, a 33% improvement. The theoretical maximum (ergodic HARQ capacity) is approximately 1.8 bps/Hz. Code combining also reduces the average number of transmissions needed per packet, from 2.1 with chase combining to 1.6 with code combining at the same operating point, reducing latency and resource consumption.

Digital Communications

Code Combining

Q: How does code combining differ from chase combining?

Chase combining (Type I HARQ) retransmits the exact same coded bits as the original transmission. The receiver combines the two copies using soft combining (averaging or maximum ratio combining of the log-likelihood ratios), gaining approximately 3 dB of SNR improvement per retransmission through diversity. The code rate stays the same. Code combining (Type II HARQ / incremental redundancy) retransmits different coded bits, specifically the parity bits that were punctured (not sent) in the original transmission. The receiver appends these new bits to the existing soft buffer, providing the decoder with more parity information and effectively lowering the code rate. This gives both SNR gain and coding gain. For example, with initial rate 3/4 and one retransmission providing the remaining parity bits to reach rate 3/8, the coding gain alone provides approximately 2 dB advantage over chase combining at the same total energy. Code combining approaches the ideal HARQ throughput bound more closely than chase combining, typically within 0.5 to 1 dB of the ergodic capacity.

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Code combining (incremental redundancy / Type II HARQ) sends different coded bits on each retransmission rather than repeating the original. Receiver merges all bits in a soft buffer, effectively lowering the code rate with each round. In 5G NR, redundancy versions (RV0/1/2/3) read from different circular buffer positions. Provides both coding gain and diversity gain, 1 to 3 dB more efficient than chase combining. Throughput: 20 to 40% higher than chase at moderate SNR.

Category: Digital Communications

Gain over chase: 1 to 3 dB

Throughput gain: 20 to 40%

Understanding Code Combining

Hybrid ARQ (HARQ) is the mechanism that makes modern wireless systems robust to channel variations. When a data packet fails its CRC check, the receiver requests retransmission, and the key question is what to retransmit. Chase combining simply repeats the same coded bits; the receiver averages them for an SNR boost. Code combining is smarter: it sends new parity bits that were generated by the channel encoder but not included in the initial transmission. These new bits give the decoder additional constraints (parity checks) that help it resolve ambiguities, effectively lowering the code rate and improving error correction capability.

The elegance of code combining lies in its adaptivity. The initial transmission uses a high code rate (say 3/4 or 5/6) that is optimistic about channel quality, maximizing throughput when conditions are good. If the channel is worse than expected and the packet fails, the retransmission lowers the effective rate to something more robust (say 1/2) by adding parity. If still unsuccessful, the second retransmission pushes it even lower (say 1/3). This progressive rate reduction automatically adapts to the actual channel condition without requiring accurate CSI at the transmitter. The system essentially starts optimistic and becomes more conservative only when needed, maximizing average throughput across varying conditions.

Code Combining Equations

Effective Code Rate After m Transmissions:
R_eff(m) = K / (m × N_tx) (assuming equal-size retransmissions)

Chase Combining SNR Gain:
SNR_combined = m × SNR_single (linear, = 3 dB per retransmission)

Code Combining Gain:
ΔG = G_code(R_eff) - G_code(R_initial) + SNR_diversity

Where K = info bits, N_tx = coded bits per transmission. Initial rate 3/4, first retransmission: R_eff = 3/8. Shannon limit at R=3/4: 5.1 dB. At R=3/8: 0.7 dB. Code combining captures ~3 dB of this 4.4 dB gap vs chase combining's ~3 dB from diversity alone.

Chase vs Code Combining Performance

Metric	Chase Combining	Code Combining	Advantage
SNR gain (per retx)	3 dB (diversity)	3 to 6 dB (coding+diversity)	Code: 1 to 3 dB more
Effective rate change	Same rate	Rate decreases	Code: adaptive
Throughput at 5 dB	~1.2 bps/Hz	~1.6 bps/Hz	Code: +33%
Avg transmissions	~2.1	~1.6	Code: 24% fewer
Buffer requirement	Store same bits	Store all unique bits	Chase: smaller buffer

Common Questions

Frequently Asked Questions

How does code combining differ from chase combining?

Chase: retransmits same bits, LLRs averaged, +3 dB SNR gain, rate unchanged. Code: retransmits different parity bits, lowers effective rate, provides coding + diversity gain. At initial rate 3/4 with one retransmission: chase stays at 3/4, code drops to 3/8, gaining ~2 dB coding advantage. Code combining within 0.5 to 1 dB of ergodic capacity.

How is it implemented in 5G NR?

LDPC encodes at mother rate 1/3. Rate matching selects bits by redundancy version (RV0/1/2/3), each starting at different circular buffer position. RV0: systematic + some parity. Retransmissions (RV2, RV3, RV1): mostly new parity. Receiver fills soft buffer positions; decoder sees lower effective rate. Soft buffer size limited by UE category.

What is the throughput gain?

At low SNR (5 dB, Rayleigh fading, initial R=3/4): code combining 1.6 bps/Hz vs chase 1.2 bps/Hz (33% improvement). Average transmissions: 1.6 vs 2.1 (24% fewer). Theoretical max: 1.8 bps/Hz. Advantage shrinks at high SNR where initial transmission usually succeeds. Code combining is standard in 5G NR, LTE, and Wi-Fi 6/7.

Related Terms

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