LFSR / PRBS – Reference Table
Primitive polynomials and sequence lengths
Primitive polynomials define maximal‑length LFSRs, producing sequences of length 2^N – 1. These sequences are widely used in PRBS generators, scramblers, BIST engines, and high‑speed serial link testing.
| PRBS Type | Polynomial (hex) | Expanded Polynomial | Sequence Length | Typical Use |
|---|---|---|---|---|
| PRBS7 | 0x48 | x⁷ + x⁶ + 1 | 2⁷ − 1 = 127 | Low‑speed serial links, basic testing |
| PRBS9 | 0x110 | x⁹ + x⁵ + 1 | 2⁹ − 1 = 511 | Legacy telecom, moderate‑length patterns |
| PRBS11 | 0x600 | x¹¹ + x⁹ + 1 | 2¹¹ − 1 = 2047 | Optical systems, stress testing |
| PRBS15 | 0x6000 | x¹⁵ + x¹⁴ + 1 | 2¹⁵ − 1 = 32767 | General‑purpose testing, scramblers |
| PRBS23 | 0x00400020 | x²³ + x¹⁸ + 1 | 2²³ − 1 | Telecom, optical, RF systems |
| PRBS31 | 0x10000008 | x³¹ + x²⁸ + 1 | 2³¹ − 1 | High‑speed serial links (10G/25G/40G/100G) |
Notes on polynomial representation
- Hex values correspond to the tap mask used in Fibonacci form.
- Expanded polynomials use Unicode exponents for readability without MathJax.
- All sequences exclude the all‑zero state.
- PRBS31 is the de‑facto standard for stressing high‑speed SERDES and CDRs.
- PRBS7 and PRBS15 are commonly used in scramblers and BIST engines.
Related pages
- LFSR & PRBS — Overview, Families & Architecture
Provides a unified view of Linear Feedback Shift Registers and Pseudo‑Random Binary Sequences, covering architectural principles, polynomial families, implementation trade‑offs, and their role in line coding, scrambling, and verification flows. - LFSR / PRBS – Mathematical Background
Algebraic foundations of LFSRs and PRBS sequences, including primitive polynomials, maximal‑length sequences, and GF(2) recurrence relations. - LFSR / PRBS – RTL Implementation Notes
Implementation details, initialization rules, parallel generation, and verification guidelines for robust LFSR and PRBS generators. - CRC — Overview, Families & Architecture
CRC computation shares the same GF(2) polynomial arithmetic used in LFSR and PRBS structures, making CRC a direct architectural extension of these mathematical foundations. - Data Path — Architecture & Fundamentals
Integration of LFSR/PRBS generators and checkers into streaming datapaths, including placement, throughput considerations, and interaction with downstream blocks. - Flow Control — Architecture & Fundamentals
Mechanisms that regulate data movement and ensure correct alignment, seeding, and checking of LFSR/PRBS sequences within streaming pipelines. - Pipelining — Architecture & Fundamentals
Architectural techniques used to balance LFSR/PRBS computation latency, improve timing closure, and maintain full‑rate throughput.
