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Parallel Scrambler Generator

  Scramblers are used in many communicaton protocols such as PCI Express, SAS/SATA, USB, Bluetooth to randomize the transmitted data. To keep this post short and focused I’ll not discuss the theory behind scramblers. For more information about scramblers see [1], or do some googling.  The topic of this post is the parallel implementation of a scrambler generator. Protocol specifications define scrambling algorithm using either hex or polynimial notation. This is not always suitable for efficient hardware or software implementation. Please read my post on parallel CRC Generator about that.

 The Parallel Scrambler Generator method that I’m going to describe has a lot in common with the Parallel CRC Generator. The difference is that CRC generator outputs CRC value, whereas Scrambler generator produces scrambled data. But the internal working of both based on the same principle.

Here is an example of a scrambler with the polynomial G(x) = x16+x5+x4+x3+1



Following is the description of the Parallel Scrambler Generator algorithm:

(1) Let’s denote N=data width, M=generator polynomial width. scrambler21

(2) Implement serial scrambler generator using given polynomial or hex notation. It’s easy to do in any programming language or script: C, Java, Perl, Verilog, etc. 

(3) Parallel Scrambler implementation is a function of N-bit data input as well as M-bit current state of the polynomial, as shown in the above figure. We’re going to build three matrices:

  • Mout (next state polynomial) as a function of Min(current state polynomial) when N=0 and
  • Nout as a function of Nin when Min=0. 
  • Nout as a function of Min when Nin=0

      Note that the polynomial next state doesn’t depend on the scrambled data, therefore we need only three matrices.


(4) Using the routine from (3) calculate scrambled data for the Mout values given Min, when Nin=0. Each Min value is one-hot encoded, that is there is only one bit set. 

(5) Build MxM matrix, Each row contains the results from (4) in increasing order. For example, 1’st row contains the result of input=0×1, 2′nd row is input=0×2, etc. The output is M-bit wide, which the polynomial width.

(6) Calculate the Nout values given Nin, when Min=0. Each Nin value is one-hot encoded, that is there is only one bit set. 

(7) Build NxN matrix, Each row contains the results from (6) in increasing order. The output is N-bit wide, which the data width.

(8) Calculate the Nout values given Min, when Nin=0. Each Min value is one-hot encoded, that is there is only one bit set. 

(9) Build MxN matrix, Each row contains the results from (7) in increasing order. The output is N-bit wide, which the data width.

(10) Now, build an equation for each Nout[i] bit: all Nin[j] and Min[k] set bits in column [i] from three matrices participate in the equation. The participating inputs are XORed together.


Nout is the parallel scrambled data.


Keep me posted if the Parallel Scrambler Generation tool works for you, or you need more clarifications on the algorithm.


  1. Scramblers on Wiki

  1. October 22nd, 2015 at 02:40 | #1

    Hi Ravikumar,

    I cannot reproduce the problem. You’re saying that the code cannot be generated ?


  2. Mike
    October 28th, 2015 at 12:23 | #2

    Is there an easy way to reverse the order the scrambler generates data? I’m messing with Rapid IO and its scrambled IDLE2 sequence and while the generator polynomial is correct, the output order is reversed from my reference model. For example, if I expect 1, 2, 3, 4 the parallel scrambler generated here outputs 4, 3, 2, 1. So I get the right sequence, but it’s backward.

    Also thanks for the site! These tools have been very helpful.

  3. October 28th, 2015 at 12:57 | #3

    Hi Mike,

    Perhaps it’s something to do with the ordering of input data. Something like bytes or words are swapped.


  4. Anurag Kumar
    December 29th, 2015 at 03:45 | #4

    Hi Evgeni,
    Thanks for this wonderful works.
    I am using your website to understand “Parallel Scrambler Generator”. But I am not able to find any information how I have to decide “data_c” assignment.
    I am using :scrambler module for data[7:0], lfsr[22:0]=1+x^2+x^5+x^8+x^16+x^21+x^23;
    But not able to understand :
    This part:
    data_c[0] = data_in[0] ^ lfsr_q[22];
    data_c[1] = data_in[1] ^ lfsr_q[21];
    data_c[2] = data_in[2] ^ lfsr_q[20] ^ lfsr_q[22];
    data_c[3] = data_in[3] ^ lfsr_q[19] ^ lfsr_q[21];
    data_c[4] = data_in[4] ^ lfsr_q[18] ^ lfsr_q[20] ^ lfsr_q[22];
    data_c[5] = data_in[5] ^ lfsr_q[17] ^ lfsr_q[19] ^ lfsr_q[21];
    data_c[6] = data_in[6] ^ lfsr_q[16] ^ lfsr_q[18] ^ lfsr_q[20] ^ lfsr_q[22];
    data_c[7] = data_in[7] ^ lfsr_q[15] ^ lfsr_q[17] ^ lfsr_q[19] ^ lfsr_q[21] ^ lfsr_q[22];

    Please can you help me to understand this part.

    What is the logic behind this and how that logic works?


  5. December 29th, 2015 at 09:07 | #5

    Hi Anurag,

    I wrote an article on how the algorithm works to generate CRC. Very similar approach is used for parallel scrambler generation as well.
    Here is the link: http://outputlogic.com/my-stuff/circuit-cellar-january-2010-crc.pdf


  6. shravan
    January 6th, 2016 at 20:45 | #6

    Hi ,
    I am writing code for self synchronous scrambler with polynomial 1+x^39+x^58.
    datawidth =64 and polywidth =58 .When iam trying to give input as all 0’s(scrambler input) the output is giving as all 64-bit ‘0s(scrambler output).
    Here i have a doubt that as per spec scrambler is defined as it will used to maintain DC balance(long sequences of 1’s or 0’s will be scrambled).so as per spec when iam giving all 1’s it is giving some scrambled data with adding 0’s to output.
    but when iam giving all 0’s it is not adding 1’s in output.

    So can you explain why it is not effecting at output for input of all 0’s.

    Shravan Kumar

  7. January 6th, 2016 at 21:01 | #7

    Hi Shravan,

    Scrambling is essentially an XOR operation on the data input and current scrambler state. If your input data is all-zero, and scrambler is initialized with zero, then the output is also zero. You need to initialize the scrambler, usually with all-Fs.


  8. Deepak Ameta
    January 17th, 2016 at 22:07 | #8

    Hi Evgeni,
    As per IEEE 802.3 std, PCS uses the self-synchronizing scrambler, and “There is no requirement on the initial value for the scrambler. The scrambler is run continuously on all payload bits”. In this condition, I have to assume my initial state of scrambler is zero then all input of 0’s generates all 0’s scrambler output. And that is violating the scrambler functionality. Please guide me to understand scrambler thoroughly.


  9. Amit Tanwar
    January 22nd, 2016 at 20:08 | #9

    I am implementing SATA scrambler. Just confused with seed value. Spec says it is FFFF. But the example given at the end using parallel scrambling method says f0f6.
    Does parallel scrambler require different seed value. Another thing I noted serial method output doesn’t match with parallel one. Not sure which one to use. Please give some pointer.

  10. luodike
    February 5th, 2016 at 17:43 | #10

    @Deepak Ameta
    this tool doesn’t work for self-synchronizing scrambler

  11. ivar
    April 29th, 2016 at 10:33 | #11

    Hi Evegni,

    Could you please add an example to clarify the above alogrithm ?

    I wanted to get some more clarification on the steps 4 – 9.
    I tried generating the lfsr using the following info
    // data[15:0], lfsr[15:0]=1+x^3+x^4+x^5+x^16;
    I am able to match the lfsr next state equations to the ones generated
    using your online generator, However the data_c[15:0] equations are not
    matching for me.


  12. Charith
    May 31st, 2016 at 21:06 | #12

    Hi Evgeni,
    Thanks for putting a very useful website. Can you please provide a descrambler for PCIE 8 GT/s spec. It uses a polynomial that is different to 2.5 and 5 GT/s rates. I have tried to generate the descrambler, by defining the polynomial at your web-site’s “user-defined” method. But, at simulation, I found that the descrambler is not working correcly.

  13. Charith
    June 8th, 2016 at 17:19 | #13

    Hi Evgeni,

    The scrambler works fine. I hadn’t given reset and enable signals correctly to it. When I fixed that it works fine. Thanks a lot for this very useful website.

  14. Anirudh
    August 10th, 2016 at 03:10 | #14

    Has anyone tried to design a pipelined scrambler ?

  15. Hens Vanderschoot
    October 21st, 2016 at 08:24 | #15

    Fantastic! Saved me a bunch of time from writing Perl or doing in manually. Thank you!!

  16. October 21st, 2016 at 08:39 | #16

    You’re welcome!

  17. Ron
    April 26th, 2017 at 13:58 | #17

    Hi Evgeni,

    I have looked at the code for your stand alone crc-gen program. Do you have a stand alone for the scrambler? I am trying to understand how to generate the MxN scrambler matrix. Would it be possible to share your algorithm or take a peek at that code?


  18. April 26th, 2017 at 14:51 | #18

    Hi Ron,

    The algorithm for scrambler is similar to the one for CRC.
    No, I don’t have scrambler code that is publicly available.


  19. Mahesh iyer
    June 18th, 2018 at 09:05 | #19

    Will scrambler code works for descrambling data also

  20. Tony
    January 12th, 2019 at 10:59 | #20

    I’m trying to generate a parallel scrambler from your site. No matter what I put in for the polynomial in step 2, hitting the generate verilog or generate vhdl button produces nothing. Is this page broken or not yet implemented?


  21. January 12th, 2019 at 11:26 | #21

    Hi Tony,

    Just tried it – the tool works fine on Chrome and IE.
    Please send me a screenshot of the parameters you put in. Another possibility is that browser blocks the results of “generate” button because the site doesn’t have SSL certificate. You might want to check developer’s window in the browser for security-related errors.


  22. Lorne
    March 13th, 2019 at 08:17 | #22

    do you have a self-synchronizing scrambler and descrambler for poly 1+x^39+x^58
    and width 26?

  23. william
    May 12th, 2021 at 16:47 | #23

    Do you have a scrambler and descrambler for lfsr[7:0]=1+x^43?

  24. william
    May 12th, 2021 at 21:59 | #24

    Do you have a scrambler and descrambler for G(X)=1+x^43 ?Input bit 8bit width.

  25. william
    May 13th, 2021 at 22:04 | #25

    Can an 8-bit input self-synchronizing scrambler and descrambler be generated? The scrambling polynomial is g(x)=X43+1.

  26. Arun Kumar
    September 25th, 2021 at 06:07 | #26


    I am working on pci gen 5.0 scramble and descramble.

    Can you please send me the link for descrambler. I want verilog code

    Data length 8,16,32,64.

  27. charles
    April 29th, 2022 at 00:38 | #27

    Your parall scrambler is based on Galois LFSR, right? How do you do if you have a fibonacci LFSR?

  28. Gucci
    March 7th, 2023 at 18:36 | #28

    Hello Evgeni,
    I am trying to learn how someone has coded a scrambler polynomial for ethernet protocol. I/O data is 9 bits wide, G(X)=1+x^4+x^15;

    // Here State14 is sent out first.
    S_w[14] = S_r[5];
    S_w[13] = S_r[4];
    S_w[12] = S_r[3];
    S_w[11] = S_r[2];
    S_w[10] = S_r[1];
    S_w[9] = S_r[0];

    S_w[8] = (use_master_poly_w == 1’b1) ? (S_r[14] ^ S_r[3]) : (S_r[14] ^ S_r[10]);
    S_w[7] = (use_master_poly_w == 1’b1) ? (S_r[13] ^ S_r[2]) : (S_r[13] ^ S_r[9]);
    S_w[6] = (use_master_poly_w == 1’b1) ? (S_r[12] ^ S_r[1]) : (S_r[12] ^ S_r[8]);
    S_w[5] = (use_master_poly_w == 1’b1) ? (S_r[11] ^ S_r[0]) : (S_r[11] ^ S_r[7]);
    S_w[4] = (use_master_poly_w == 1’b1) ? (S_r[10] ^ S_r[14] ^ S_r[3]) : (S_r[10] ^ S_r[6]);
    S_w[3] = (use_master_poly_w == 1’b1) ? (S_r[9 ] ^ S_r[13] ^ S_r[2]) : (S_r[9 ] ^ S_r[5]);
    S_w[2] = (use_master_poly_w == 1’b1) ? (S_r[8 ] ^ S_r[12] ^ S_r[1]) : (S_r[8 ] ^ S_r[4]);
    S_w[1] = (use_master_poly_w == 1’b1) ? (S_r[7 ] ^ S_r[11] ^ S_r[0]) : (S_r[7 ] ^ S_r[3]);
    S_w[0] = (use_master_poly_w == 1’b1) ? (S_r[6 ] ^ S_r[10] ^ S_r[14] ^ S_r[3]) : (S_r[6 ] ^ S_r[2]);


    But when I generate the Verilog code using your tool, the equations are different. Can you please tell me what I am missing here?

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  1. December 19th, 2015 at 06:58 | #1