How is the lifting size Z selected?

The lifting size Z determines the dimensions of the LDPC parity-check matrix by scaling the base graph. The base graph defines the structure (which variable nodes connect to which check nodes) and Z determines the size of each sub-matrix (Z times Z identity or shifted identity matrices). To encode K_payload information bits, the system finds the smallest valid K = k_b * Z that is at least K_payload, which means finding the smallest Z such that Z >= ceil(K_payload / k_b). The valid Z values form 8 sets: Set 1 has Z = 2, 4, 8, 16, 32, 64, 128, 256 (base 2); Set 2 has Z = 3, 6, 12, 24, 48, 96, 192, 384 (base 3); and similarly for base values 5, 7, 9, 11, 13, 15. Each set spans Z from its base value up to base times 128 (or base times 256 for sets 1 and 2). The implementation selects the set and Z value that minimizes the padding (filler bits) needed to fill the code block to exactly K = k_b * Z bits. This padding is inserted as known zero bits, which the decoder treats as perfectly reliable (infinite LLR), slightly improving decoding performance.

How does base graph selection affect code block size?

5G NR defines two LDPC base graphs with different characteristics. Base graph 1 (BG1) has 46 rows and 68 columns (22 systematic columns, 4 core parity columns, 42 extension parity columns), giving a maximum code block information size of 22*Z = 8,448 bits at Z=384, and mother code rate of 22/68 = 1/3. BG1 is selected when the transport block size is large (above approximately 3,824 bits after CRC) and the code rate is above 1/4. It provides the best performance at moderate to high code rates (1/3 to 8/9) and large block sizes, which is the typical operating point for high-throughput eMBB traffic. Base graph 2 (BG2) has 42 rows and 52 columns (10 systematic columns, 4 core parity columns, 38 extension parity columns), giving maximum information size of 10*Z = 3,840 bits and mother code rate of 10/52 = approximately 1/5. BG2 is selected for small transport blocks (below approximately 3,824 bits) or very low code rates (below 1/4), which occurs in URLLC traffic, control channels, and cell-edge coverage scenarios.

How does code block size affect LDPC decoding performance?

Larger code blocks generally provide better error correction performance due to the law of large numbers: random channel impairments average out more effectively over longer codewords. At a code rate of 1/2, increasing the code block size from 1,000 to 8,000 bits typically provides 0.3 to 0.5 dB improvement in required SNR for a target block error rate of 1%. However, larger blocks also increase decoding latency (more iterations needed and each iteration processes more bits) and memory requirements (the decoder must store the entire code block's log-likelihood ratios). For URLLC applications requiring less than 1 ms latency, smaller code blocks from BG2 are preferred even at a slight performance penalty. The filler bits added during segmentation to reach a valid K size slightly benefit decoding because they are known bits (zero LLR set to infinity), effectively increasing the code rate at the decoder without actually transmitting those bits. This free side information can improve performance by 0.05 to 0.1 dB.

Digital Communications

Code Block Size

/kohd blok size/

Code block size (K) is the information bit count per LDPC-encoded block in 5G NR, calculated as K = k_b × Z where k_b is 22 (BG1) or 10 (BG2) and Z is the lifting size (2 to 384, from 51 valid values in 8 sets per 3GPP TS 38.212). Maximum K: 8,448 bits (BG1) and 3,840 bits (BG2). BG1 for large TBs and high code rates (>1/4); BG2 for small TBs, low rates, and URLLC. Filler bits pad to valid K with infinite LLR at decoder.

Category: Digital Communications

Max K (BG1): 8,448 bits

Max K (BG2): 3,840 bits

Understanding Code Block Size

The code block size is a fundamental parameter of the 5G NR LDPC channel coding chain, directly affecting error correction performance, decoding latency, and hardware complexity. Unlike turbo codes in LTE (which could handle arbitrary block sizes through internal interleaver design), LDPC codes in 5G NR use a structured parity-check matrix whose dimensions are determined by the lifting size Z. This means the code block size is constrained to specific values K = k_b × Z, where k_b is the number of systematic columns in the base graph and Z is one of 51 valid lifting sizes.

The lifting mechanism provides an elegant way to scale the LDPC code across a wide range of block sizes (44 to 8,448 bits for BG1) using a single base graph design. The base graph defines the code's error correction properties (threshold, error floor, decoding convergence), while the lifting size Z scales the matrix dimensions without changing these properties. This means the same LDPC decoder architecture can handle all code block sizes by simply changing Z, which corresponds to changing the shift values in the sub-matrices from Z×Z identity matrices. Hardware implementations use barrel shifters that can accommodate any valid Z value, enabling a single decoder IP to cover the full range of 5G NR code block sizes.

Code Block Size Formulas

Information Bits per Code Block:
K = k_b × Z (k_b = 22 for BG1, 10 for BG2)

Total Codeword Length:
N = n_b × Z (n_b = 68 for BG1, 52 for BG2)

Mother Code Rate:
R_mother = k_b/n_b = 22/68 ≈ 1/3 (BG1) or 10/52 ≈ 1/5 (BG2)

Lifting sizes Z ∈ {2,3,4,5,...,384} from 8 sets: {2×2^j}, {3×2^j}, {5×2^j}, {7×2^j}, {9×2^j}, {11×2^j}, {13×2^j}, {15×2^j}. Select smallest Z giving K ≥ payload+CRC.

Code Block Size Examples

Base Graph	Z	K (info bits)	N (codeword)	Use Case
BG1	384	8,448	26,112	Max throughput eMBB
BG1	256	5,632	17,408	Large TBs, moderate BW
BG1	128	2,816	8,704	Medium TBs
BG2	384	3,840	19,968	Low rate, cell edge
BG2	16	160	832	URLLC small payload

Common Questions

Frequently Asked Questions

How is lifting size Z selected?

Find smallest Z where k_b×Z ≥ payload+CRC. Z from 51 valid values in 8 sets (base × 2^j, bases: 2,3,5,7,9,11,13,15). Implementation selects set minimizing padding (filler bits). Fillers are known zeros treated as infinite LLR at decoder, giving 0.05 to 0.1 dB free gain. Single decoder handles all Z via configurable barrel shifters.

How does base graph selection affect size?

BG1: k_b=22, max K=8,448, R_mother=1/3. Selected for large TBs (>3,824 bits) and code rate >1/4. Best for eMBB. BG2: k_b=10, max K=3,840, R_mother=1/5. For small TBs, rate <1/4, URLLC, and control channels. BG2 provides better performance at very low rates and short blocks.

How does size affect decoding performance?

Larger blocks: 0.3 to 0.5 dB better at R=1/2 (random impairments average out). But more latency and memory. For URLLC (<1 ms), smaller BG2 blocks preferred despite slight performance penalty. K=8,448 vs K=1,000: ~0.4 dB improvement at BLER 1%, but 8x more decode time.

Related Terms

← Code Block Segmentation Code Combining →