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Application of product of codes of Read-Solomona for correction of errors in an optical computer memory

Read-Solomona codes belong to the class of MDR-CODES which admit regular coding (a code word contains the informational symbols in an explicit form) and provide the greatest possible minimum signal distance for set nи to [21, 22, 23].

Decoding of code words of Rs-codes is based on the solution of system of the linear algebraic equations over final field Galua [24, 25, 26, 27] and includes following stages:

1) Scaling of a syndrome of errors with use of circuit design Gornera. Thus everyone a syndrome component looks the following image:

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2) Scaling of a polynomial of locators of errors Λ (%) and quantity of errors in a code word accepted from the channel. For this purpose the iterative algorithm Berlekempa-Messi consistently accepting on an entry components of a syndrome, computed on the previous stage can be used. Thus on each iteration the discrepancy representing a difference predicted komponentoj of a syndrome, gained by means of a current polynomial of locators and arrived on the given iteration komponentoj a syndrome is computed. The discrepancy is computed by formula:

3) the Finding of locators of errors by means of procedure CHenja consisting in search of zero result of substitution of value return to a locator of an error in a polynomial Λ (x).

5) Process of correction of errors is reduced to formation of a polynomial of errors on the basis of found before locators and values of errors and correction of a polynomial of the code word accepted from the channel.

For correction of the errors originating at reading of the information from disks DVD, use of product of codes of Read-Solomona (Reed-Solomon Product Code, RSPC) [28, 29] is provided. The code word of product can be presented in the form of a matrix:

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Lines of a matrix are words of a code of Read-Solomona with parametres (nh, kh, dh). Matrix columns represent words of the Rs-code with parametres (nv, kv, dv). The three (n, k, d) defines word length (n), its dimensions of a quantity (k) and the minimum signal distance (d).

Number garantirovanno corrected symbols the Rs-code equally tc = [(d — 1) ∕2J. For the Rs-code (208, 192, 17) with symbols from field Galua GF (28) used in DVD, a maximum number garantirovanno corrected erroneous symbols equally 8. For the Rs-code (182, 172, 11), also used in DVD, the maximum number garantirovanno corrected errors is equated 5.

The minimum signal distance of product of these codes will be equal dh* dv, and number garantirovanno corrected erroneous symbols (octad) such proizvedeniemgde dhи dv -

The minimum signal distance for horizontal and vertical code words, accordingly. The number garantirovanno corrected erroneous symbols product of codes of Read-Solomona, used in DVD, is equal 93.

The coded data unit which has been written down in one sector of disk DVD, is resulted in drawing 1. The informational symbols of the block at first are coded by the Rs-code (208, 192, 17) on a vertical, and then coding by the Rs-code (182, 172, 11) on level is carried out.

In drawing 1 following designations are used:

jv - Number of a vertical code word;

jh - Number of a horizontal code word;

iv - Symbol number in a vertical code word;

ih - Symbol number in a horizontal code word.

The Fig. 1 Data unit of sector DVD coded by product of codes of Read-Solomona

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A source: Krivonos Alexey Vladimirovich. METHODS, ALGORITHM And the DEVICE of CORRECTION of ERRORS In the OPTICAL COMPUTER MEMORY. The DISSERTATION on competition of a scientific degree of a Cand.Tech.Sci. Kursk - 2018. 2018

More on topic Application of product of codes of Read-Solomona for correction of errors in an optical computer memory:

  1. the APPLICATION 1. Results of imitating modelling of product of codes of Read-Solomona used in optical disks DVD, by means of the developed device on model of the channel with clustering of errors
  2. RESEARCH OF THE DEVICE OF CORRECTION OF ERRORS IN THE OPTICAL COMPUTER MEMORY BY IMITATING MODELLING
  3. the Structurally functional organisation of the device of correction of errors in an optical computer memory
  4. Sampling of quantity of iterations for effective correction of errors in channels of an optical computer memory
  5. 1.5 Devices of correction of errors for an optical computer memory
  6. WORKING OUT OF THE DEVICE OF CORRECTION OF ERRORS IN THE OPTICAL COMPUTER MEMORY
  7. Methods of correction of the errors originating in channels of record - of reproduction of an optical computer memory
  8. THE ANALYSIS OF METHODS, ALGORITHMS AND HARDWARE OF CORRECTION OF ERRORS IN THE OPTICAL COMPUTER MEMORY
  9. 3.2 Estimation of complexity and fast operations of the device of correction of errors in an optical computer memory
  10. 1.4.1 Standard dvuhetapnyj a method of decoding of product of codes of Read-Solomona
  11. 1.5.2 Device of iterative decoding of product of codes of Read-Solomona
  12. 2.3 Vertically-persevering method of decoding of product of codes of Read-Solomona
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