What is c_init used for in LTE/5G?

c_init seeds the Gold code sequence generator for multiple purposes: (1) PDSCH/PUSCH scrambling: makes data appear noise-like, randomizing inter-cell interference. c_init includes RNTI (user identity) and cell ID, so each user in each cell gets a unique scrambling sequence. (2) DMRS generation: demodulation reference signals for channel estimation. c_init includes slot number and symbol index, so DMRS changes every slot for time-varying channel tracking. (3) CSI-RS: channel state information reference signals. c_init includes the CSI-RS resource configuration ID. (4) PRACH preamble: random access preambles. c_init selects which Zadoff-Chu root sequence to use. By changing c_init, the network creates orthogonal or quasi-orthogonal signal spaces for different users, cells, and time instants.

How does the Gold code generator work?

The pseudo-random sequence c(n) is defined in 3GPP TS 38.211 as: c(n) = (x1(n+Nc) + x2(n+Nc)) mod 2. x1 and x2 are length-31 m-sequences (maximum-length linear feedback shift register sequences). x1 is initialized to x1(0)=1, x1(n)=0 for n=1..30 (fixed). x2 is initialized from c_init: the 31-bit binary representation of c_init sets x2(0)..x2(30). Nc = 1600 (initial offset to ensure independence of initial transient). The generator produces 2^31 - 1 = 2,147,483,647 bits before repeating. Different c_init values produce different x2 sequences, which when XORed with the fixed x1, produce different Gold codes. Gold codes have bounded cross-correlation, providing multi-user interference averaging.

Why does c_init matter for testing?

For protocol testing and UE conformance testing, knowing the exact c_init is essential for: (1) Descrambling received data: the test equipment must generate the same scrambling sequence as the transmitter. Wrong c_init = complete data loss (descrambled data looks like noise). (2) DMRS detection: test equipment must know c_init to generate the expected DMRS and perform channel estimation. Wrong c_init = no channel estimate = no demodulation. (3) Interference modeling: accurate interference simulation requires correct c_init for each interfering cell/user. In 5G NR conformance testing (3GPP TS 38.521): test cases specify exact c_init values for all configured channels. Test equipment vendors (Keysight, R&S, Anritsu) implement the c_init computation per 3GPP specification.

5G NR / LTE

C-INIT

/see-ih-nit/ c_init

31-bit seed for Gold code pseudo-random sequence generator (3GPP TS 38.211). Seeds scrambling (PDSCH: c_init = n_RNTI×2¹⁴ + q×2¹³ + n_ID), DMRS, CSI-RS, and PRACH sequences. Different c_init = orthogonal sequences for multi-user/multi-cell separation. Period: 2³¹-1 bits. N_c = 1600 offset.

Bits: 31

Period: 2³¹-1

Spec: TS 38.211

Understanding C-INIT

Every scrambled bit in an LTE or 5G NR transmission depends on c_init. This 31-bit number is computed from parameters like the user's RNTI, the cell ID, the slot number, and the channel type. It seeds the Gold code generator that produces the pseudo-random scrambling sequence. Both transmitter and receiver must compute the same c_init to produce the same sequence; otherwise, descrambling fails and all data is lost.

C-INIT Formulas

C-INIT:
31-bit seed for Gold code pseudo-random sequence generator (3GPP TS 38.211). Seeds scrambling (PDSCH: c init = n RNTI ×2 14 + q×2 13 +...

Key specifications:
-1 bits | 16 bits | 0 dB | 1 mW | 30 dB

Power: P(dBm) = 10log(P_mW), 0dBm = 1mW

C-INIT by Channel/Signal

Channel	c_init Depends On	Purpose	Updates
PDSCH	RNTI, q, n_ID	Data scrambling	Per TB
PUSCH	RNTI, n_ID	UL scrambling	Per TB
DMRS	Slot, symbol, SCID	Channel est.	Per slot
CSI-RS	Slot, symbol, config	CSI measurement	Per resource
PDCCH	n_ID	Control scrambling	Semi-static

Key Equations

Decibel conversion:
Power: dB = 10log(P₂/P₁)
Voltage: dB = 20log(V₂/V₁)

dBm to watts:
P(W) = 10^{(dBm−30)/10}
0 dBm = 1 mW, +30 dBm = 1 W

Wavelength:
λ = c/f = 300/f(MHz) meters

Comparison

Aspect	C-INIT Spec	Typical Range	Impact	Design Note
Primary function	31-bit seed for Gold code pseudo-random...	Application-dep.	Critical	Verify in sim
Operating range	Seeds scrambling (PDSCH: c init = n RNTI...	Application-dep.	Critical	Verify in sim
Performance	Different c init = orthogonal sequences...	Application-dep.	Critical	Verify in sim
Integration	Understanding C-INIT Every scrambled bit...	Application-dep.	Critical	Verify in sim
Trade-off	This 31-bit number is computed from para...	Application-dep.	Critical	Verify in sim

Common Questions

Frequently Asked Questions

Uses?

Seeds Gold code for: PDSCH/PUSCH scrambling (per-user, per-cell), DMRS (channel estimation, per-slot), CSI-RS, PRACH preambles. Different c_init = orthogonal sequences. Multi-user/multi-cell separation.

Generator?

Two length-31 m-sequences XORed. x1: fixed init. x2: initialized from c_init (31 bits). Nc=1600 offset. Period: 2^31-1 bits. Gold codes have bounded cross-correlation for interference averaging.

Testing?

Wrong c_init = complete data loss (descrambled data = noise). Test equipment must compute exact c_init per 3GPP spec. Conformance tests (TS 38.521) specify exact values. Critical for UE validation.

Related Terms

← C/I Ratio C/N Ratio →