Talk:Barker code

Why 2 codes of length 4 ?

I do not understand why there is two codes of length 4 in the table. The second is indeed a cycle shift of the first one, so they are identical. —Preceding unsigned comment added by 147.171.132.88 (talk) 13:13, 13 May 2011 (UTC)

Unlike maximum length sequences, Barker codes are not cyclic. They are generally transmitted in a very short short burst, with a long pause between each burst.

• The first code of length 4 would be transmitted as the pattern .... 0 0 0 0 +1 +1 −1 +1 0 0 0 0 0 0 ...
• The second code of length 4 would be transmitted as the pattern .... 0 0 0 0 +1 +1 +1 −1 0 0 0 0 0 0 ...

There is no way to "shift" that first pattern to make it identical to the second one.

All the known finite length codes that meet the low autocorrelation criteria are listed in that table. Cyclic shifts of those codes (except for the length-4 exception you pointed out) do not, in general, meet the low autocorrelation criteria necessary to be considered a Barker code. How can we edit the article to make this more clear? --DavidCary (talk) 04:15, 10 April 2012 (UTC)

no longer Barker codes exist?

Mathworld says it is conjectured that no longer Barker codes exist. Shouldn't the article be changed to reflect that, since mathworld is the only source listed? —Preceding unsigned comment added by 146.6.203.178 (talk) 22:37, 24 March 2009 (UTC)

+-+-+

i have a question of the barker code could we follow the rule to the barker code 5 (+-+-+)?

Alas, no. The sequence +-+-+ does not qualify as a Barker code. The autocorrelation of a Barker code is required to have all off-peak autocorrelations of either -1, 0, or +1. The autocorrelation coefficients of the +1 -1 +1 -1 +1 sequence are: ... 0 +1 -2 +3 -4 +5 -4 +3 -2 +1 0 0 0 0 0 ... The off-peak autocorrelations of -2, +3, and -4 indicate that +-+-+ is not a Barker code. --DavidCary (talk) 04:15, 10 April 2012 (UTC)

optimal Barker code

Currently this article states

Here is a table of all known optimal Barker codes, where negations and reversals of the codes have been omitted. Optimal is defined as having a maximum autocorrelation of 1 (when codes are not aligned).

That implies there exists some "Barker code" that is not an "optimal Barker code". I think that every Barker code is an "optimal" Barker code. So I am removing all mentions of "optimal". (If there exists some "Barker code" that is not an "optimal Barker code", please revert my edit and list that example in the article.) --68.0.124.33 (talk) 02:42, 1 August 2008 (UTC)

Method to verify codes

Maybe it would be usefull to add this simple method, by which it is posibble to verify a code if it is a Barker-code:

Let there be N numbers a1, a2, a3, ......, aN where every a equals either +1 or -1.

Pick a number k where 1 <= k <N.

Write down the first k a's, in order, then write down the last k a's in order. For k=3 you would write down

a1, a2, a3

a(N-2), a(N-1), aN.

Now multiply corresponding numbers and add (dot product):

a1 a(N-2) + a2 a(N-1) + a3 aN.

It's a Barker code if that sum is always (for every k) equal to 0, 1 or -1.

from: [1] --Grapestain (talk) 23:18, 26 May 2009 (UTC)

Mismatch between introduction and list of sequences

In the introduction it says that there are a total of eight Barker codes and three of them meeting the stronger condition

$c_{v}=0,-1$.

A reference to a paper by Borwein and Mossinghoff is given.

But the next section lists nine sequences, and four of those meet the stronger condition. The reason for this mismatch is that in the given reference, the sequence [1 -1] is not listed as a Barker code. Since I don't have access to the original paper by Barker, I cannot tell who is "wrong" here, Wikipedia or Borwein/Mossinghoff. Consequently, I don't want to decide on my own what the correct modification to the article is: delete the sequence [1 -1] from the list (hence making wikipedia conformant to the cited article), or adding a note about this mismatch. Any suggestions? — Preceding unsigned comment added by 217.24.206.253 (talk) 14:04, 17 January 2013 (UTC)

better RMS performance?

In reference to the text

A Barker code has a maximum autocorrelation sequence which has sidelobes no larger than 2, and which thus has better RMS performance than the codes below.

How can a barker code have better RMS performance than the code below when the codes below are barker codes? Dsandber (talk) 11:27, 23 July 2013 (UTC)

Missing barker code

Based on this code there are two different 11-bit barker codes:

import numpy as np

barker1 = [+1,-1,+1,+1,-1,+1,+1,+1,-1,-1,-1] barker2 = [+1,+1,+1,-1,-1,-1,+1,-1,-1,+1,-1]

print np.correlate( barker1, barker1, "full") print np.correlate( barker2, barker2, "full")

Someone want to verify and if true correct it? --Dsandber (talk) 05:31, 24 July 2013 (UTC)

These two 11-bit Barker codes need not count as two separate codes as they are merely a negation and reversal of each other. The article indicates it is not listing the four permutations of negation and reversal but each such permutation will also satisfy the Barker code requirements. No correction is needed for this section. 24.107.77.26 (talk) 04:03, 1 October 2013 (UTC)

The sidelobe level of amplitude of the Barker codes

"The sidelobe level of amplitude of the Barker codes is 1/N that of the peak signal" I disagree with this statement. 1. Amplitude of Barker codes is 1 (+1 or -1). Sidelobe level is feature of autocorrelation function. 2. Sidelobe level of Barker codes is 0 or 1, so 1/N is relation of maximum sidelobe level to peak. — Preceding unsigned comment added by Gluttton (talk • contribs) 11:44, 22 January 2017 (UTC)

Confusing figure?

Figure presenting 802.11 is confusing. According to the standard "the symbol duration shall be exactly 11 chips long". The symbol (data bit) is being spread by Barker code in front of the modulator. 79.184.105.8 (talk) 07:50, 14 July 2021 (UTC)

Proposed addition to include a History Section

During and after WWII digital technology became a key subject for research e.g. for radar, missile and gun fire control and encryption. In the 1950’s scientists were trying various methods around the world to reduce errors in transmissions using code and to synchronise the received data. The problem being transmission noise, time delay and accuracy of received data. In 1949 the mathematician [Claude E Shannon] published an article [A mathematical Theory of Communication] which laid out the basic elements of communication. In it he discusses the problems of noise.

Shannon realised that “communication signals must be treated in isolation from the meaning of the messages that they transmit” and laid down the theoretical foundations for digital circuits. “The problem of communication was primarily viewed as a deterministic signal-reconstruction problem: how to transform a received signal, distorted by the physical medium, to reconstruct the original as accurately as possible”. (Ref: Quanta Magazine, How Claude Shannon invented the future).

https://www.quantamagazine.org/how-claude-shannons-information-theory-invented-the-future-20201222/

In 1953 RH Barker published a paper demonstrating how this problem to synchronise the data in transmissions could be overcome. The process is described in “Group Synchronisation of Binary Digital Systems”. When used in data transmissions the receiver can read and if necessary correct the data to be error free by auto and cross correlation i.e. by achieving zero autocorrelation except at the incidence position using specific codes. The Barker sequence utilised a technique of auto correlation and cross correlation which at the time produced great interest, particularly in the United States as his method solved the problem, initiating a huge leap forward in telecommunications. The process has remained at the forefront of data transmission and telemetry and is now a very well known industry standard, still being researched.

“In a pioneering examination of group synchronization of binary digital systems, Barker reasoned it would be desirable to start with an autocorrelation function having very low sidelobes. The governing code pattern, he insisted, could be unambiguously recognized by the detector. To assure this premise, Barker contended the selected pattern should be sufficiently unlikely to occur by chance, in a random series of noise generated bits” (1.)p13 Please comment. Windswept (talk) 10:09, 8 November 2022 (UTC)

References

Examples of Application

There is a vast number of examples to add. Also many variants have been developed to improve specific fields of research. This addition should give the reader a better insight and understanding. Windswept (talk) 09:26, 6 October 2023 (UTC)

Barker's Algorithm

The final section entitled "Barker's Algorithm" seems incomplete. There is no description of the algorithm and how it relates to Metropolis Hastings, which is an algorithm to sample from probability distribution. If nothing else more detail and a reference is needed. VictorSMiller (talk) 01:00, 7 March 2024 (UTC)