Introduction¶

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

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

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

Known Bugs And Assumptions¶

None.

Usage¶

This chapter provides examples of how to use the library.

/* 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);

/* 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);

/* 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);

/* 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);

/* 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]);}

/* Release resources */free_rs(rs_decoder);

Structures¶

This chapter contains the autogenerated documentation of the structureswhich are used in the Reed-Solomon Library and are relevant for adeveloper.

structrs_codec¶

rs codec data

Definition

struct rs_codec {  int mm;  int nn;  uint16_t *alpha_to;  uint16_t *index_of;  uint16_t *genpoly;  int nroots;  int fcr;  int prim;  int iprim;  int gfpoly;  int (*gffunc)(int);  int users;  struct list_head list;};

Members

mm

Bits per symbol

nn

Symbols per block (= (1<<mm)-1)

alpha_to

log lookup table

index_of

Antilog lookup table

genpoly

Generator polynomial

nroots

Number of generator roots = number of parity symbols

fcr

First consecutive root, index form

prim

Primitive element, index form

iprim

prim-th root of 1, index form

gfpoly

The primitive generator polynominal

gffunc

Function to generate the field, if non-canonical representation

users

Users of this structure

list

List entry for the rs codec list

structrs_control¶

rs control structure per instance

Definition

struct rs_control {  struct rs_codec *codec;  uint16_t buffers[];};

Members

codec

The codec used for this instance

buffers

Internal scratch buffers used in calls to decode_rs()

structrs_control *init_rs(int symsize, int gfpoly, int fcr, int prim, int nroots)¶

Create a RS control struct and initialize it

Parameters

intsymsize

the symbol size (number of bits)

intgfpoly

the extended Galois field generator polynomial coefficients,with the 0th coefficient in the low order bit. The polynomialmust be primitive;

intfcr

the first consecutive root of the rs code generator polynomialin index form

intprim

primitive element to generate polynomial roots

intnroots

RS code generator polynomial degree (number of roots)

Description

Allocations use GFP_KERNEL.

Public Functions Provided¶

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

voidfree_rs(structrs_control * rs)¶

Free the rs control structure

Parameters

structrs_control*rs

The control structure which is not longer used by thecaller

Description

Free the control structure. Ifrs is the last user of the associatedcodec, free the codec as well.

structrs_control *init_rs_gfp(int symsize, int gfpoly, int fcr, int prim, int nroots, gfp_t gfp)¶

Create a RS control struct and initialize it

Parameters

intsymsize

the symbol size (number of bits)

intgfpoly

the extended Galois field generator polynomial coefficients,with the 0th coefficient in the low order bit. The polynomialmust be primitive;

intfcr

the first consecutive root of the rs code generator polynomialin index form

intprim

primitive element to generate polynomial roots

intnroots

RS code generator polynomial degree (number of roots)

gfp_tgfp

Memory allocation flags.

structrs_control *init_rs_non_canonical(int symsize, int (*gffunc)(int), int fcr, int prim, int nroots)¶

Allocate rs control struct for fields with non-canonical representation

Parameters

intsymsize

the symbol size (number of bits)

int(*)(int)gffunc

pointer to function to generate the next field element,or the multiplicative identity element if given 0. Usedinstead of gfpoly if gfpoly is 0

intfcr

the first consecutive root of the rs code generator polynomialin index form

intprim

primitive element to generate polynomial roots

intnroots

RS code generator polynomial degree (number of roots)

intencode_rs8(structrs_control * rsc, uint8_t * data, int len, uint16_t * par, uint16_t invmsk)¶

Calculate the parity for data values (8bit data width)

Parameters

structrs_control*rsc

the rs control structure

uint8_t*data

data field of a given type

intlen

data length

uint16_t*par

parity data, must be initialized by caller (usually all 0)

uint16_tinvmsk

invert data mask (will be xored on data)

The parity uses a uint16_t data type to enablesymbol size > 8. The calling code must take care of encoding of thesyndrome result for storage itself.

intdecode_rs8(structrs_control * rsc, uint8_t * data, uint16_t * par, int len, uint16_t * s, int no_eras, int * eras_pos, uint16_t invmsk, uint16_t * corr)¶

Decode codeword (8bit data width)

Parameters

structrs_control*rsc

the rs control structure

uint8_t*data

data field of a given type

uint16_t*par

received parity data field

intlen

data length

uint16_t*s

syndrome data field, must be in index form(if NULL, syndrome is calculated)

intno_eras

number of erasures

int*eras_pos

position of erasures, can be NULL

uint16_tinvmsk

invert data mask (will be xored on data, not on parity!)

uint16_t*corr

buffer to store correction bitmask on eras_pos

The syndrome and parity uses a uint16_t data type to enablesymbol size > 8. The calling code must take care of decoding of thesyndrome result and the received parity before calling this code.

Note

The rs_control structrsc contains buffers which are used for

decoding, so the caller has to ensure that decoder invocations areserialized.

Returns the number of corrected symbols or -EBADMSG for uncorrectableerrors. The count includes errors in the parity.

intencode_rs16(structrs_control * rsc, uint16_t * data, int len, uint16_t * par, uint16_t invmsk)¶

Calculate the parity for data values (16bit data width)

Parameters

structrs_control*rsc

the rs control structure

uint16_t*data

data field of a given type

intlen

data length

uint16_t*par

parity data, must be initialized by caller (usually all 0)

uint16_tinvmsk

invert data mask (will be xored on data, not on parity!)

Each field in the data array contains up to symbol size bits of valid data.

intdecode_rs16(structrs_control * rsc, uint16_t * data, uint16_t * par, int len, uint16_t * s, int no_eras, int * eras_pos, uint16_t invmsk, uint16_t * corr)¶

Decode codeword (16bit data width)

Parameters

structrs_control*rsc

the rs control structure

uint16_t*data

data field of a given type

uint16_t*par

received parity data field

intlen

data length

uint16_t*s

syndrome data field, must be in index form(if NULL, syndrome is calculated)

intno_eras

number of erasures

int*eras_pos

position of erasures, can be NULL

uint16_tinvmsk

invert data mask (will be xored on data, not on parity!)

uint16_t*corr

buffer to store correction bitmask on eras_pos

Each field in the data array contains up to symbol size bits of valid data.

Note

The rc_control structrsc contains buffers which are used for

decoding, so the caller has to ensure that decoder invocations areserialized.

Returns the number of corrected symbols or -EBADMSG for uncorrectableerrors. The count includes errors in the parity.

Credits¶

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

Copyright 2002, Phil Karn, KA9QMay 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 fortesting. Thanks a lot.

The following people have contributed to this document:

Thomas Gleixnertglx@linutronix.de