# Reed solomon calculator

The Berlekamp—Massey algorithm is an algorithm that will find the shortest linear feedback shift register LFSR for a given binary output sequence. The algorithm will also find the minimal polynomial of a linearly recurrent sequence in an arbitrary field. The field requirement means that the Berlekamp—Massey algorithm requires all non-zero elements to have a multiplicative inverse.

The Berlekamp—Massey algorithm is an alternative to the Reed—Solomon Peterson decoder for solving the set of linear equations.

The error locator polynomial C x for L errors is defined as:. The goal of the algorithm is to determine the minimal degree L and C x which results in all syndromes. Algorithm: C x is initialized to 1, L is the current number of assumed errors, and initialized to zero. N is the total number of syndromes. B x is a copy of the last C x since L was updated and initialized to 1. Each iteration of the algorithm calculates a discrepancy d.

At iteration k this would be:. If d is zero, the algorithm assumes that C x and L are correct for the moment, increments mand continues. If d is not zero, the algorithm adjusts C x so that a recalculation of d would be zero:. The x m term shifts B x so it follows the syndromes corresponding to b.

The algorithm also needs to increase L number of errors as needed. If L equals the actual number of errors, then during the iteration process, the discrepancies will become zero before n becomes greater than or equal to 2 L.

The algorithm from Masseyp.

## Write a simple Reed Solomon Calculator Program

The following is the Berlekamp—Massey algorithm specialized for the binary finite field F 2 also written GF 2. The field elements are '0' and '1'. The division operator reduces to the identity operation i. From Wikipedia, the free encyclopedia. Not to be confused with Berlekamp's algorithm.

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Categories : Error detection and correction Cryptanalytic algorithms. Hidden categories: CS1: long volume value Articles with German-language sources de. Namespaces Article Talk. Views Read Edit View history. By using this site, you agree to the Terms of Use and Privacy Policy.I'm looking to have a program developed which can detect a reed-solomon sector from a group of byte sectors sampled from individual members of a RAID array.

The intent of the program is for determining parity rotation in failed RAID 6 arrays. The program would need to have a basic GUI with the following functions:. Based on number of members, have boxes in the next screen to paste in values pulled from same sector of each RAID member preferably as GREP expression, but other ways such as ANSI might work too as long as it's a format which can be copied from a hex editor such as winhex.

Once all values are pasted in, have a "Calculate" button to be pressed. Program will then brute force calculate reed solomon value for every possible combination of the sectors less two for the P XOR parity and Q Reed Solomon members and check that value against the remaining values pasted in to determine which one is the Reed Solomon sector.

This can all be done under the hood, no visual output required. Program then indicates which of the sectors was the Reed Solomon, and which other blocks were used to calculate it so the P block can be indicated as well.

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This project will require the programmer to have good understanding of the math involved with reed solomon calculations. The program doesn't need to be "pretty", just a basic interface to put in the values and get the results back as well as some basic logo branding.

Skills: MathematicsProgrammingSoftware Architecture. See more: the p. Dear client, how are you? Looking forward to your response. Hi I am an expert programmer. I can develop on multiple of platforms in multiple language. I understand the project description and do the job quickly. Please contact me to discuss further. Hi Client, How are you? I have developed over 70 apps for 5 years. Very interesting project. Do you have sample data to test the algorithm on?

This would be very helpful. Thank you for reading this proposal. I'am an Electrical Engineer with specialization in Electronics Department and my work in embedded systems involve delivering clients top notch products which cover MCUssensor More.

The email address is already associated with a Freelancer account. Enter your password below to link accounts:. Freelancer Jobs Mathematics Write a simple Reed Solomon Calculator Program I'm looking to have a program developed which can detect a reed-solomon sector from a group of byte sectors sampled from individual members of a RAID array.

The program would need to have a basic GUI with the following functions: 1.Documentation Help Center. The output genpoly is a Galois field array that represents the coefficients of the generator polynomial in order of descending powers.

Specify the codeword length, nand message length, k. Create the narrow-sense generator polynomial for the [n,k] Reed-Solomon code. Create the generator polynomial of a Reed-Solomon code with respect to the default primitive polynomial. Display the error-correcting capability of the code. Create the generator polynomial for the [ nk ] Reed-Solomon code. Create the narrow-sense generator polynomial of a Reed-Solomon code. Specify the output data type as a double-precision array.

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Create the narrow-sense generator polynomial for the [ nk ] Reed-Solomon code. For more information, see Limitations. Message length, specified as a positive integer.

Primitive polynomial, specified as a positive integer. For more information, see Default Primitive Polynomials. Output format of genpolyspecified as:. For more information, see Working with Galois Fields. Generator polynomial coefficients in descending order, returned as a Galois field array or double-precision array. This table lists the default primitive polynomial used for each Galois field array GF 2 m.

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For more information, see Primitive Polynomials and Element Representations. All inputs must be constants. Expressions or variables are allowed if their values do not change. A modified version of this example exists on your system. Do you want to open this version instead? Choose a web site to get translated content where available and see local events and offers. Based on your location, we recommend that you select:.

Select the China site in Chinese or English for best site performance. Other MathWorks country sites are not optimized for visits from your location. Toggle Main Navigation. Search Support Support MathWorks.See Reed-Solomon calculator.

Galois arithmetic limits the number of data plus ECC bytes codewords to a maximum total of Larger barcodes are presented as a series of blocks each less than bytes. ECC88 Systematic layout. Layouts of this form cannot be deduced by program! In this case, Blocks 1,2 contain 11 data bytes, Blocks 3,4 contain 12 data bytes. The Reed Solomon calculations are computed for each block. ECC22 etc. See Reed Solomon Calculator.

## QRCODE block layout

QRCODE bit masking The following barcodes all have the same content and are equally valid but each bit is masked using a number of formula depending on the bit row and column position. The final symbols are then scanned for unwanted "artefacts" and rated accordingly. The symbol with the least number of deprecated features is selected as the final symbol and the MASK INDEX used in this case 5 is recorded in the appropriate part of the symbol.

This process is computationally expensive and many vendors simply skip this stage and select a mask index at random. In a "noisy" reader enviroment this may make recognition difficult.If not filtered, the main lobe will have a bandwidth of twice the Nyquist bandwidth. If unfiltered, the bandwidth of the main lobe is twice the Nyquist bandwidth or twice the symbol rate.

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Very useful calculator. It helped me understand enough that I could figure it out on my own. While most calculator on the web are tied to a particular operation mode like satellite or microwave, this tiny tool is very flexible and accommodates various input options for pretty much any mode of operation.

This calculator is also extremely useful for amateur radio operators wishing to deploy digital modulation schemes. The Nyquist bandwidth is the minimum bandwidth than can be used to represent a signal. This is the correct bandwidth for transmitters which deploy a Nyquist bandwidth filter, which is the case for most professional transmitters.

Sorry, your blog cannot share posts by email.An introduction to Reed-Solomon codes: principles, architecture and implementation. Reed-Solomon codes are block-based error correcting codes with a wide range of applications in digital communications and storage. Reed-Solomon codes are used to correct errors in many systems including:. The Reed-Solomon encoder takes a block of digital data and adds extra "redundant" bits.

Errors occur during transmission or storage for a number of reasons for example noise or interference, scratches on a CD, etc. The Reed-Solomon decoder processes each block and attempts to correct errors and recover the original data. The number and type of errors that can be corrected depends on the characteristics of the Reed-Solomon code.

### f(x) ÷ gp(x)

Reed Solomon codes are a subset of BCH codes and are linear block codes. A Reed-Solomon code is specified as RS n,k with s -bit symbols. This means that the encoder takes k data symbols of s bits each and adds parity symbols to make an n symbol codeword.

There are n-k parity symbols of s bits each. The following diagram shows a typical Reed-Solomon codeword this is known as a Systematic code because the data is left unchanged and the parity symbols are appended :. Each codeword contains code word bytes, of which bytes are data and 32 bytes are parity. For this code:.

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The decoder can correct any 16 symbol errors in the code word: i. Reed-Solomon codes may be shortened by conceptually making a number of data symbols zero at the encoder, not transmitting them, and then re-inserting them at the decoder.

Example : Thecode described above can be shortened toThe encoder takes a block of data bytes, conceptually adds 55 zero bytes, creates acodeword and transmits only the data bytes and 32 parity bytes. The amount of processing "power" required to encode and decode Reed-Solomon codes is related to the number of parity symbols per codeword. A large value of t means that a large number of errors can be corrected but requires more computational power than a small value of t.

One symbol error occurs when 1 bit in a symbol is wrong or when all the bits in a symbol are wrong. Example : RScan correct 16 symbol errors. In the worst case, 16 bit errors may occur, each in a separate symbol byte so that the decoder corrects 16 bit errors. In the best case, 16 complete byte errors occur so that the decoder corrects 16 x 8 bit errors.

Reed-Solomon codes are particularly well suited to correcting burst errors where a series of bits in the codeword are received in error. Reed-Solomon algebraic decoding procedures can correct errors and erasures.

An erasure occurs when the position of an erred symbol is known. A decoder can correct up to t errors or up to 2t erasures. Erasure information can often be supplied by the demodulator in a digital communication system, i. The decoder will detect that it cannot recover the original code word and indicate this fact. The probability of each of the three possibilities depends on the particular Reed-Solomon code and on the number and distribution of errors. The advantage of using Reed-Solomon codes is that the probability of an error remaining in the decoded data is usually much lower than the probability of an error if Reed-Solomon is not used.

This is often described as coding gain. This can be achieved by boosting the power of the transmitter or by adding Reed-Solomon or another type of Forward Error Correction.

Reed-Solomon allows the system to achieve this target BER with a lower transmitter output power. The power "saving" given by Reed-Solomon in decibels is the coding gain. Reed-Solomon encoding and decoding can be carried out in software or in special-purpose hardware. Reed-Solomon codes are based on a specialist area of mathematics known as Galois fields or finite fields. A Reed-Solomon encoder or decoder needs to carry out these arithmetic operations.

These operations require special hardware or software functions to implement.The XOR function satisfies two important conditions:. Using these properties of XOR function allows one to calculate one of the missing values given all the other. RAID 6 uses two different functions to calculate the parity.

When there are one or two parity functions which should be placed on several disks, several different patterns can arise. The trivial solution is to put parity only on one disk.

Reed Solomon Encoding - Computerphile

In such case we get a RAID 4 which has a low write performance because each write operation affects a disk with parity, which becomes a bottleneck. It is much more efficient to place the parity evenly on all disks. In case of one parity there is only left and right rotation.

When two parity functions are used, one more parameter is required - position of first parity function relative to the second one, that is, it is required to determine what the parity is left and what is right. It should be noted that there is no guarantee that the parity will always move by one column per row. In case of RAID5 it's pretty pointless to move the parity more than by one, so it is unlikely that you will ever deal with such configuration. In case of RAID6 such configuration does exist and is called wide pace.

For example, Promise controllers use this parity layout. Additionally, there is no guarantee that the size of parity block is the same as the size of data block. If the parity block is larger than block with data we get an array with so called delayed parity which is used in HP Smart Array controllers. MS Storage Spaces has another interesting specific - it changes the disk order arbitrarily over the long intervals, about hundreds of megabytes.

Note: The bottleneck of RAID4 is a disk storing parity, however it is so only if you deal with the identical disks. Continue to "Write hole". If A and B occupy the same number of bits, C also occupies that number of bits.

Parity Placement When there are one or two parity functions which should be placed on several disks, several different patterns can arise.