# Bit error rate tester using fast parallel generation of linear recurring sequences

## Abstract

A fast method for generating linear recurring sequences by parallel linear recurring sequence generators (LRSGs) with a feedback circuit optimized to balance minimum propagation delay against maximal sequence period. Parallel generation of linear recurring sequences requires decimating the sequence (creating small contiguous sections of the sequence in each LRSG). A companion matrix form is selected depending on whether the LFSR is right-shifting or left-shifting. The companion matrix is completed by selecting a primitive irreducible polynomial with 1's most closely grouped in a corner of the companion matrix. A decimation matrix is created by raising the companion matrix to the (n*k).sup.th power, where k is the number of parallel LRSGs and n is the number of bits to be generated at a time by each LRSG. Companion matrices with 1's closely grouped in a corner will yield sparse decimation matrices. A feedback circuit comprised of XOR logic gates implements the decimation matrix in hardware. Sparse decimation matrices can be implemented with minimum number of XOR gates, and therefore a minimum propagation delay through the feedback circuit. The LRSG of the invention is particularly well suited to use as a bit error rate tester on high speed communication lines because it permitsmore »

- Inventors:

- Issue Date:

- Research Org.:
- Sandia National Lab. (SNL-CA), Livermore, CA (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1174312

- Patent Number(s):
- 6,560,727

- Application Number:
- 09/426,073

- Assignee:
- Sandia Corporation (Albuquerque, NM) SNL-L

- DOE Contract Number:
- AC04-94AL85000

- Resource Type:
- Patent

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 42 ENGINEERING; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS

### Citation Formats

```
Pierson, Lyndon G., Witzke, Edward L., and Maestas, Joseph H.
```*Bit error rate tester using fast parallel generation of linear recurring sequences*. United States: N. p., 2003.
Web.

```
Pierson, Lyndon G., Witzke, Edward L., & Maestas, Joseph H.
```*Bit error rate tester using fast parallel generation of linear recurring sequences*. United States.

```
Pierson, Lyndon G., Witzke, Edward L., and Maestas, Joseph H. Tue .
"Bit error rate tester using fast parallel generation of linear recurring sequences". United States. https://www.osti.gov/servlets/purl/1174312.
```

```
@article{osti_1174312,
```

title = {Bit error rate tester using fast parallel generation of linear recurring sequences},

author = {Pierson, Lyndon G. and Witzke, Edward L. and Maestas, Joseph H.},

abstractNote = {A fast method for generating linear recurring sequences by parallel linear recurring sequence generators (LRSGs) with a feedback circuit optimized to balance minimum propagation delay against maximal sequence period. Parallel generation of linear recurring sequences requires decimating the sequence (creating small contiguous sections of the sequence in each LRSG). A companion matrix form is selected depending on whether the LFSR is right-shifting or left-shifting. The companion matrix is completed by selecting a primitive irreducible polynomial with 1's most closely grouped in a corner of the companion matrix. A decimation matrix is created by raising the companion matrix to the (n*k).sup.th power, where k is the number of parallel LRSGs and n is the number of bits to be generated at a time by each LRSG. Companion matrices with 1's closely grouped in a corner will yield sparse decimation matrices. A feedback circuit comprised of XOR logic gates implements the decimation matrix in hardware. Sparse decimation matrices can be implemented with minimum number of XOR gates, and therefore a minimum propagation delay through the feedback circuit. The LRSG of the invention is particularly well suited to use as a bit error rate tester on high speed communication lines because it permits the receiver to synchronize to the transmitted pattern within 2n bits.},

doi = {},

journal = {},

number = ,

volume = ,

place = {United States},

year = {2003},

month = {5}

}