# Reed-Solomon Library Programming Interface

Thomas
Gleixner

          tglx@linutronix.de

2004
Thomas Gleixner

This documentation is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License version 2 as published by the Free Software Foundation.

This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

You should have received a copy of the GNU General Public License along with this program; if not, write to the Free Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA

For more details see the file COPYING in the source distribution of Linux.

## Introduction

The generic Reed-Solomon Library provides encoding, decoding and error correction functions.

Reed-Solomon codes are used in communication and storage applications to ensure data integrity.

This documentation is provided for developers who want to utilize the functions provided by the library.

## Known Bugs And Assumptions

None.

## Usage

This chapter provides examples of how to use the library.

### Initializing

The init function init_rs returns a pointer to an rs decoder structure, which holds the necessary information for encoding, decoding and error correction with the given polynomial. It either uses an existing matching decoder or creates a new one. On creation all the lookup tables for fast en/decoding are created. The function may take a while, so make sure not to call it in critical code paths.

    /* the Reed Solomon control structure */
    static struct rs_control *rs_decoder;

    /* Symbolsize is 10 (bits)
     * Primitive polynomial is x^10+x^3+1
     * first consecutive root is 0
     * primitive element to generate roots = 1
     * generator polynomial degree (number of roots) = 6
     */
    rs_decoder = init_rs (10, 0x409, 0, 1, 6);

### Encoding

The encoder calculates the Reed-Solomon code over the given data length and stores the result in the parity buffer. Note that the parity buffer must be initialized before calling the encoder.

The expanded data can be inverted on the fly by providing a non-zero inversion mask. The expanded data is XOR'ed with the mask. This is used e.g. for FLASH ECC, where the all 0xFF is inverted to an all 0x00. The Reed-Solomon code for all 0x00 is all 0x00. The code is inverted before storing to FLASH so it is 0xFF too. This prevents that reading from an erased FLASH results in ECC errors.

The databytes are expanded to the given symbol size on the fly. There is no support for encoding continuous bitstreams with a symbol size != 8 at the moment. If it is necessary it should be not a big deal to implement such functionality.

    /* Parity buffer. Size = number of roots */
    uint16_t par[6];
    /* Initialize the parity buffer */
    memset(par, 0, sizeof(par));
    /* Encode 512 byte in data8. Store parity in buffer par */
    encode_rs8 (rs_decoder, data8, 512, par, 0);

### Decoding

The decoder calculates the syndrome over the given data length and the received parity symbols and corrects errors in the data.

If a syndrome is available from a hardware decoder then the syndrome calculation is skipped.

The correction of the data buffer can be suppressed by providing a correction pattern buffer and an error location buffer to the decoder. The decoder stores the calculated error location and the correction bitmask in the given buffers. This is useful for hardware decoders which use a weird bit ordering scheme.

The databytes are expanded to the given symbol size on the fly. There is no support for decoding continuous bitstreams with a symbolsize != 8 at the moment. If it is necessary it should be not a big deal to implement such functionality.

#### Decoding with syndrome calculation, direct data correction

    /* Parity buffer. Size = number of roots */
    uint16_t par[6];
    uint8_t  data[512];
    int numerr;
    /* Receive data */
    .....
    /* Receive parity */
    .....
    /* Decode 512 byte in data8.*/
    numerr = decode_rs8 (rs_decoder, data8, par, 512, NULL, 0, NULL, 0, NULL);

#### Decoding with syndrome given by hardware decoder, direct data correction

    /* Parity buffer. Size = number of roots */
    uint16_t par[6], syn[6];
    uint8_t  data[512];
    int numerr;
    /* Receive data */
    .....
    /* Receive parity */
    .....
    /* Get syndrome from hardware decoder */
    .....
    /* Decode 512 byte in data8.*/
    numerr = decode_rs8 (rs_decoder, data8, par, 512, syn, 0, NULL, 0, NULL);

#### Decoding with syndrome given by hardware decoder, no direct data correction.

Note: It's not necessary to give data and received parity to the decoder.

    /* Parity buffer. Size = number of roots */
    uint16_t par[6], syn[6], corr[8];
    uint8_t  data[512];
    int numerr, errpos[8];
    /* Receive data */
    .....
    /* Receive parity */
    .....
    /* Get syndrome from hardware decoder */
    .....
    /* Decode 512 byte in data8.*/
    numerr = decode_rs8 (rs_decoder, NULL, NULL, 512, syn, 0, errpos, 0, corr);
    for (i = 0; i < numerr; i++) {
    	do_error_correction_in_your_buffer(errpos[i], corr[i]);
    }

### Cleanup

The function free_rs frees the allocated resources, if the caller is the last user of the decoder.

    /* Release resources */
    free_rs(rs_decoder);

## Structures

This chapter contains the autogenerated documentation of the structures which are used in the Reed-Solomon Library and are relevant for a developer.

!Iinclude/linux/rslib.h

## Public Functions Provided

This chapter contains the autogenerated documentation of the Reed-Solomon functions which are exported.

!Elib/reed_solomon/reed_solomon.c

## Credits

The library code for encoding and decoding was written by Phil Karn.

    		Copyright 2002, Phil Karn, KA9Q
     		May be used under the terms of the GNU General Public License (GPL)

The wrapper functions and interfaces are written by Thomas Gleixner.

Many users have provided bugfixes, improvements and helping hands for testing. Thanks a lot.

The following people have contributed to this document:

Thomas Gleixnertglx@linutronix.de