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AN #114 - Getting started in Data Transmission and Error detection with Correction Print
Getting started in Data Transmission and Error detection with Correction

This application note was submitted by Srikanth Kamath. Email panther@vasnet.co.in

All is explained in the program you can download. It is also shown below.

'AN ******************Error detection and correction***************************
' Application Note  *
' Getting started in Data Transmission and Error detection with Correction *
' using BASCOM AVR *
'===============================================================================
' Encodes 21 -bit Data Word Into 32 -bit Extended Bch 32.21 Word *
' *
' This code is used in the POCSAG protocol specification for pagers. *
' *
' In this specific case, there is no need to use the Berlekamp-Massey *
' algorithm, since the error locator polynomial is of at most degree 2. *
' Instead, we simply solve by hand two simultaneous equations to give *
' the coefficients of the error locator polynomial in the case of two *
' errors. In the case of one error, the location is given by the first  *
' syndrome. *
' *
' This program derivates from the original bch2.c, which was written *
' to simulate the encoding/decoding of primitive binary BCH codes. *
' Part of this program is adapted from a Reed-Solomon encoder/decoder *
' program, 'rs.c', to the binary case. *
'  *
'-------------------------------------------------------------------------------
' Extended Code Bch 32.21 Correction Using Zeh Functions *
' The Idea And The Original Algorithm Were Proposed By K. Borisov *
' C Source Code(c)vlv *
'*******************************************************************************
' Ported to BASCOM AVR by M/S PACTINDIA on 27.04.2002 *
' Written by Srikanth Kamath; e-mail: panther@vasnet.co.in *
' *
' (c) Copyright 2002 Panther Electronics ; www.pactindia.com/bascom.htm *
' *
' COPYRIGHT NOTICE: This program is free for non-commercial purposes. *
' You may implement this program for any non-commercial application. You may *
' also implement this program for commercial purposes, provided that you *
' obtain my written permission. Any modification of this program is covered *
' by this copyright.  *
' *
'===============================================================================
'*******************************************************************************
' The Bch 32.21 Codeword Is Treated As Long Int Data Size is 21 bits *
' The Function Corrects Up To 2 Errors And Detects At Least 3 Errors. *
' The Error Value Is Amount Of Errors(0 , 1 , 2).  *
' If The Error Is Not Correctable , Error Value Is 0xff And The Codeword *
' Is Not Changed. *
'*******************************************************************************
' The Encoding part is of size 700byte this should gointo the transmitting uC *
' The Decoding part is of size 1900byte this should gointo the Reciever uC *
' The Test part is the routine that you must change to in the TX uC to encode *
' and similarly the Test part must change in the TR uC to decode *
'===============================================================================
' BUGS: *
' Fixed on 5.5.2002,  *
' The error are now correctly reported 0,1,2 or 255 * *
' 27.4.2002 The corrected_data is either +1 or -1 at times from actual *
' encodded_data But this does not effect the decode or error correction *
' Also the error no reported is not related to no of error but detected *
'-------------------------------------------------------------------------------
' Warranty & Disclaimer: *
' *
' We do not guarantee that this module is free from defects or bug's in normal *
' use/service, and that these module will perform to the current specification *
' in accordance with, and subject to, the company’s standard warranty which *
' is detailed in Panther Electronics Purchase order Acknowledgement. *
'  *
' We assumes no responsibility for the use of any circuits / code described in *
' this book / e-book/ manual, nor does the company assumes responsibility for *
' the functioning of undescribed features or parameters. *
' *
' In absence of a written agreement to the contrary, Panther Electronics *
' assumes no liability with respect to the use of semiconductors devices/codes *
' described and used in this module for product design or infringements of *
' patents or copyrights of third parties. *
'  *
' These are control modules /codes only and not tested with for full *
' functionality with the controlled units and products. These modules are not *
' authorised for use as critical components or systems and the use as such *
' implies that the user bears all risk of such use. *
'*******************************************************************************
' Many Many Thanks to  *
' Mark Albert's, Eric Baron, Udo, Jack Tidwel and all other who have helped *
'==============================================================================*

' Change this to Suit you AVR
$regfile = "8515def.dat"
'$dbg
' Note this code requires HW10, SS32 and FRAME 43
Declare Function Encodebch(datas As Long) As Long
Declare Function Correctbch(encodedbchword As Long) As Long

'***************The test program ***********************************************
' This test is to Show how tHe BCH encoding of 21bit data packet helps in
' error detection and correction of error in asyncrony data transmission
' this BCH encoding and Decoding provides error correction upto 2 error per
' packet of 21bit. Hence the chances of usefull and purpose full transmission
' is garrented

Dim Inputdata As Long
' This is the data to be transmitted
Dim Temp As Byte , Cnt As Byte ' temp variables used
Dim Just_tmp As Long  ' temp variables used
Dim Corrupted_data As Long
' This is the received data
Dim Decoded_data As Long
' this is the decoded data = inputdata
Dim Encoded_data As Long
' this is the corrected data
Dim Result As Byte
' This is the error no
' NOTE: If Result = &HFF the error could not be corrected hence discard the
' Received data

Do

Main
:
 Inputdata
= 0
 
' get some random data in
 
For Cnt = 1 To 2
 
Shift Inputdata , Left , 8
 Temp
= Rnd(255)
 Inputdata
= Inputdata Xor Temp
 
Next

 
'** / / Truncate To 21 Bit
 Inputdata
= Inputdata And &H1FFFFFF
 
'** / / Encode To Bch 32.21
 Encoded_data
= Encodebch(inputdata)

 
'/ / Corrupt Data(2 Random Errors)
 Corrupted_data
= Encoded_data
 
'Corrupted_data is the received transmission data
 Temp
= Rnd(255)
 Temp
= Temp And &H1F
 
Set Corrupted_data.temp
 Just_tmp
= Corrupted_data
 Temp
= Rnd(255)
 Temp
= Temp And &H1F
 
Set Corrupted_data.temp
 
Print " Encoded Data with first error " ; Just_tmp ; " with second Second error " ; Corrupted_data

 
'// Correct Data
 
'Call Correctbch(corrupted_data)
 Just_tmp
= Correctbch(corrupted_data)

 
'// Decode Data
 
Print "Corrupted_data " ; Corrupted_data ; " EncodedWord " ; Encoded_data ; " Corrected_data " ; Just_tmp
 Decoded_data
= Just_tmp
 
' This is the the required to get back the corrected data
 
Shift Decoded_data , Right , 11
 
' Can be shift this to Correctbch itself, but kept it here to check and test

 
If Result <> &HFF Then
 
If Inputdata <> Decoded_data Then
 
Print " Error check this"
 
Print "---------Srikanth Kamath T___________**********"
 
Else
 
Print "Inputdata " ; Inputdata ; " Decode Data " ; Decoded_data ; " No of Error Corrected " ; Result
 
Print "---------Decode Sucessful___________**********"
 
End If
 
Else
 
Print "---------Decode not possible___________**********" ; " No of Error more than 2: " ; Result
 
End If
'Goto Main
Loop

'***************Function Encoded the 21 bit InputData to 32 bit BCH_word********
' This Function Encoded the 21 bit InputData to 32 bit BCH_word

Function Encodebch(datas As Long)

Local Tmp_enc As Long , Ci As Byte , Ltmp_enc As Long

 Ltmp_enc
= Datas
 
'/ / Divide By Polynom
 
For Ci = 0 To 20
 
Shift Ltmp_enc , Left , 1
 Tmp_enc
= Ltmp_enc And &H200000
 
If Tmp_enc <> 0 Then
 Ltmp_enc
= Ltmp_enc Xor &H1B4800
 
End If
  
Next

 
'/ / Allign The Remainder
 
Shift Ltmp_enc , Right , 10
 Ltmp_enc
= Ltmp_enc And &H7FE

 
' / / Add Data
 Tmp_enc
= Datas
 
Shift Tmp_enc , Left , 11
 Ltmp_enc
= Ltmp_enc Or Tmp_enc
 Encodebch
= Ltmp_enc
 
' / / Calculate Parity
 Ci
= 0
 
While Ltmp_enc <> 0
 Tmp_enc
= Ltmp_enc And 1
 
'debug
 Ci
= Ci Xor Low(tmp_enc)
' Tmp_enc2 = Tmp_enc2 Xor Tmp_enc
' Ci = Low(tmp_enc2)
 
Shift Ltmp_enc , Right , 1
 
Wend

 
' / / Add Parity
 Encodebch
= Encodebch Or Ci
End Function

'-------------------------------------------------------------------------------
'END OF*********Function Encoded the 21 bit InputData to 32 bit BCH_word********

'***************The decoding and error correction start*************************
'*************************Correction Itself*************************************
' Using the zeh function
Declare Function Makesyndrome(x As Long , Byval Polynom As Byte) As Byte
Declare Function Inverbit(bch_word As Long , Byval Bitno As Byte) As Long

Function Correctbch(encodedbchword As Long)
Local Sa As Byte , Sb As Byte , Parity As Byte , Dist As Byte , Tmplong As Long , Tmp As Byte , Ltmp As Long

 Ltmp
= Encodedbchword
 
' / / Calculate Syndromes A And B
 Sa
= Makesyndrome(ltmp , &H05)
 Sb
= Makesyndrome(ltmp , &H1D)

 
' / / Calculate Parity
  Parity
= 0

 
While Ltmp <> 0
 Tmplong
= Ltmp And 1
 Tmp
= Low(tmplong)
 Parity
= Parity Xor Tmp
 
Shift Ltmp , Right , 1
 
Wend

 
' / / Check Syndromes
 
If Sa = 0 And Sb <> 0 Then
 Result
= &HFF
 Correctbch
= Encodedbchword
 
Exit Function
 
End If

 
If Sb = 0 And Sa <> 0 Then
 Result
= &HFF
 Correctbch
= Encodedbchword
  
Exit Function
 
End If

 
'// If Both Syndromes Are 0(no Code Errors)
 
If Sa = 0 And Sb = 0 Then
 
If Parity = 0 Then
 
'// No Errors
 Result
= 0
 Correctbch
= Encodedbchword
 
Exit Function
 
End If
 
'debug
 Correctbch
= Encodedbchword Xor 1
 Result
= 1
 
Exit Function
 
End If

 Sa
= Lookup(sa , Table_sa)
 Sb
= Lookup(sb , Table_sb)
 
'// If Both Syndromes Are Indicating One Error
 
If Sa = Sb Then
 Correctbch
= Inverbit(encodedbchword , Sa)
 
' debug 1
 
' If(parity! = 0) Return 1 ; / / One Error
 
'Tmp = 0
 
'If Parity = 0 Then
 
' Set Tmp.0
 
'Else
 
' Reset Tmp.0
 
'End If
 
'--- debug 1
 
If Parity <> 0 Then
 Result
= 1
 
Exit Function
 
End If
 
' debug 1
 Correctbch
= Correctbch Xor 1
 Result
= 2
 
Exit Function
 
End If

 
'// More Then Two Errors - Not Correctable
  
If Parity <> 0 Then
 Result
= &HFF
 Correctbch
= Encodedbchword
 
Exit Function
 
End If

 Dist
= Sa - Sb
 
'// Modulo 1f
 Tmp
= Dist And &H80
 
If Tmp <> 0 Then
 Dist
= Dist + &H1F
 
End If

 
'// Find Distance Between Errors
 Dist
= Lookup(dist , Table_dist)

 
'// Not Correctable
 
If Dist = &HFF Then
 Result
= &HFF
 Correctbch
= Encodedbchword
 
Exit Function
 
End If

 
'// Correct 1 -st Error Location
 Tmp
= Lookup(dist , Dist_correction_table)
 Sa
= Sa - Tmp

 
'// Modulo 31
 Tmp
= Sa And &H80
 
If Tmp <> 0 Then

 Sa
= Sa + &H1F
 
End If

 
'/ / Correct 1 -st Error
 Tmp
= Sa + 1
 Correctbch
= Inverbit(encodedbchword , Tmp)

 
'// Find 2 -nd Error Location
 Sa
= Sa + Dist

  
'// Modulo 31
 
If Sa >= 31 Then
 Sa
= Sa - 31
 
End If

 
'//Correct 2 -nd Error
 Tmp
= Sa + 1
 Correctbch
= Inverbit(correctbch , Tmp)
 Result
= 2
End Function

'-------------------------------------------------------------------------------
'END OF*******************Correction Itself*************************************


'************************Divide By Polynom**************************************

'Sub Makesyndrome(x As Long , Byval Polynom As Byte)
Function Makesyndrome(x As Long , Byval Polynom As Byte)
Local Tmp_syn As Long , Cntr As Byte , L_polynom As Long , Tmp_syn2 As Long

 Tmp_syn
= X And &HFFFFFFFE
 L_polynom
= Polynom
  
Shift L_polynom , Left , 27

 
' / / Calculate The Syndrome
 
For Cntr = 0 To 30
 Tmp_syn2
= Tmp_syn And &H80000000
 
If Tmp_syn2 <> 0 Then
 
Shift Tmp_syn , Left , 1
 Tmp_syn
= Tmp_syn Xor L_polynom
 
Else
 
Shift Tmp_syn , Left , 1
 
End If
 
Next
 
Shift Tmp_syn , Right , 27
 Makesyndrome
= Tmp_syn

End Function
'-------------------------------------------------------------------------------
'END OF******************Divide By Polynom**************************************


'***************Invert Bit At The Position Bitno********************************

'Sub Inverbit(bch_word As Long , Byval Bitno)
Function Inverbit(bch_word As Long , Byval Bitno As Byte)
Local Tmp_inver As Long
 Tmp_inver
= 0
 
Set Tmp_inver.bitno
 Inverbit
= Bch_word Xor Tmp_inver
End Function
'-------------------------------------------------------------------------------
'END OF*********Invert Bit At The Position Bitno********************************

'****************Syndrome A Error Position Table********************************

Table_sa
:
Data &H00 , &H1B , &H1C , &H0E , &H1D , &H01 , &H0F , &H07,
Data &H1E , &H19 , &H02 , &H17 , &H10 , &H04 , &H08 , &H13,
Data &H1F , &H06 , &H1A , &H0D , &H03 , &H12 , &H18 , &H16,
Data &H11 , &H15 , &H05 , &H0C , &H09 , &H0A , &H14 , &H0B

Table_sb
:
Data &H00 , &H1B , &H1C , &H10 , &H1D , &H05 , &H11 , &H02,
Data &H1E , &H16 , &H06 , &H0C , &H12 , &H14 , &H03 , &H19,
Data &H1F , &H0E , &H17 , &H0A , &H07 , &H08 , &H0D , &H09,
Data &H13 , &H18 , &H15 , &H0B , &H04 , &H01 , &H1A , &H0F

Table_dist
:
Data &HFF , &HFF , &HFF , &H03 , &HFF , &HFF , &H06 , &H0B,
Data &HFF , &HFF , &HFF , &HFF , &H0C , &HFF , &H09 , &H08,
Data &HFF , &H0E , &HFF , &H0A , &HFF , &HFF , &HFF , &H04,
Data &H07 , &H05 , &HFF , &H02 , &H0D , &H01 , &H0F , &HFF

Dist_correction_table
:
Data &HFF , &H13 , &H06 , &H1E , &H0B , &H03 , &H1C , &H17,
Data &H15 , &H11 , &H05 , &H14 , &H18 , &H0F , &H0E , &H19