ccsdsRSDecode

Decode CCSDS-complaint RS codes

Since R2021a

Syntax

[decoded,cnumerr,ccode] = ccsdsRSDecode(code,k)

[decoded,cnumerr,ccode] = ccsdsRSDecode(code,k,i)

[decoded,cnumerr,ccode] = ccsdsRSDecode(code,k,i,s)

Description

[decoded,cnumerr,ccode] = ccsdsRSDecode(code,k) decodes the received signal in code by using a (255, k) Reed-Solomon (RS) decoder with the generator polynomial, as defined in the Consultative Committee for Space Data Systems (CCSDS) 131.0-B-3 Section 4 [1]. k is the number of symbols in the decoded message. The function returns the decoded message, decoded, the number of corrected errors, cnumerr, and the corrected version of code, ccode.

For a description of CCSDS RS code decoding, see CCSDS RS Code Decoding.

[decoded,cnumerr,ccode] = ccsdsRSDecode(code,k,i) specifies the interleaving depth, i. code consists of i RS codewords of length 255 bytes.

[decoded,cnumerr,ccode] = ccsdsRSDecode(code,k,i,s) specifies the shortened message length, s.

Examples

Encode and Decode Full-length CCSDS RS Encoded Message

Generate a full-length encoded Reed-Solomon (RS) codeword, introduce random errors, and decode the result using a Consultative Committee for Space Data Systems (CCSDS) RS decoder.

Generate a random message of length k.

k = 223;
msg = randi([0 255],k,1);

Encode the message by using a CCSDS RS encoder.

code = ccsdsRSEncode(msg,k);

Generate 15 random error symbols and 15 unique random locations to insert these errors.

err = randi([1 255],15,1);
errLoc = randperm(255,15);
errVec = zeros(255,1);
errVec(errLoc) = err;

Introduce error symbols in the encoded message.

rxBytes = bitxor(code,errVec);

Decode the encoded symbols introduced with errors by using CCSDS RS decoder.

[decoded,v,ccode] = ccsdsRSDecode(rxBytes, k);

Display the number of corrected errors.

disp(v)

    15

Decode CCSDS RS Codeword with Burst Errors

Generate an full-length encoded Reed-Solomon (RS) codeword, introduce burst of errors, and decode the result using a Consultative Committee for Space Data Systems (CCSDS) RS decoder.

Specify the message length k and interleaving depth, i.

k = 239;
i = 5;

Generate a column vector of random message bits. Encode the message by using a CCSDS RS encoder.

msg = randi([0 255],k*i,1);
code = ccsdsRSEncode(msg,k,i);

Generate 30 random error symbols.

err = randi([1 255],30,1);
errVec = zeros(255*i,1);

Introduce burst errors from location 52 to 81.

errVec(52:81) = err;
rxBytes = bitxor(code,errVec);

Decode the encoded symbols introduced with burst errors by using a CCSDS RS decoder.

[decoded,v,ccode] = ccsdsRSDecode(rxBytes,k,i);

Display the number of corrected errors.

disp(v)

    30

Encode-Decode CCSDS RS Shortened Codeword

Encode-decode a bit-input shortened CCSDS RS encoded codeword with interleaving, in the presence of additive white Gaussian noise (AWGN) channel.

Encode the bit-input shortened message using CCSDS RS encoder.

k = 239;  % Message length
s = 219;  % Shortened message length
i = 5;    % Interleaving depth
msg = logical(randi([0 1],s*i*8,1)); % Datatype is logical for bit input
codeBits = ccsdsRSEncode(msg,k,i,s);

QAM modulate a signal, add AWGN, and then demodulate to get the LLR bits.

M = 4;
txSig = qammod(double(codeBits),M, ...
     InputType="bit",UnitAveragePower=true);  % QAM modulation
snr = 10;                                     % SNR in dB
rxSig = awgn(txSig,snr,"measured",0);        % AWGN addition
llr = qamdemod(rxSig,M,"OutputType", ...
   "approxllr","UnitAveragePower",true, ...
   NoiseVariance=10.^(-snr/10));              % LLR demapper

Demodulate the RS encoded codeword using the CCSDS RS decoder.

[decoded,v,ccode] = ccsdsRSDecode(llr<0,k,i,s);

Calculate the BER.

berCalc = comm.ErrorRate;
errInfo = berCalc(msg,decoded);
numErr = int32(errInfo(2));      % Number of erroneous bits

Display the error information.

fprintf('Number of errors after decoding = %d.\n', numErr);

Number of errors after decoding = 0.

fprintf('Number of errors corrected = %d.\n', int32(v));

Number of errors corrected = 7.

Input Arguments

code — Encoded message

column vector of integers in the range [0, 255]

Encoded message, specified as a column vector of integers in the range [0, 255].

The elements and the size of the column vector depends on the data type of the input message.

• For a logical data type, each element in the vector is either 0 or 1.

• For a uint8 or double data type, each element is an integer symbol in GF(2^m), in the range [0, 255]. m is the number of bits in each symbol.

Input Message Type	Size of code
	Data Type of code Is logical	Data Type of code Is uint8 or double
Full length input message	8*255*i	255*i
Shortened input message	8*i*(255 – k + s)	i*(255 – k + s)

Data Types: double | uint8 | logical

k — Number of symbols in decoded message

223 | 239

Number of symbols in the decoded message, specified as 223 or 239.

Data Types: double | uint8

i — Interleaving depth

1 (default) | positive integer

Interleaving depth, specified as a positive integer. The default value, 1, corresponds to no interleaving.

code consists of i RS codewords of length 255 bytes.

Data Types: double | uint8

s — Shortened message length

k (default) | integer in the range [1, k]

Shortened message length, specified as an integer in the range [1, k].

Data Types: double | uint8

Output Arguments

decoded — Decoded message

column vector

Decoded message, returned as a column vector. Each element represents decoding the corresponding element in input code. The data type of decoded is the same as that of code.

The size of the column vector depends on the data type of code.

Input Message Type	Size of decoded
	Data Type of code Is logical	Data Type of code Is uint8 or double
Full length input message	8*k*i	k*i
Shortened input message	8*s*i	s*i

When the value of output cnumerr is –1, decoded is equal to the first k elements of code.

cnumerr — Number of corrected errors

integer in the range [-1, (n – k) ∕ 2]

Number of corrected errors, returned as an integer in the range [-1, (n – k) ∕ 2], where n is the codeword length. The value of n is set to 255 according to CCSDS 131.0-B-3 Section 4 [1].

A value of –1 in cnumerr indicates the failure of the decoder to correct the errors.

ccode — Corrected version of code

column vector

Corrected version of code, returned as a column vector. The length of ccode is same as the length of code. The data type of ccode is the same as that of code.

When the value of output cnumerr is –1, ccode is equal to code.

More About

CCSDS RS Code Decoding

CCSDS RS codes are powerful burst error-correcting codes. These are most commonly used as forward error-correcting (FEC) codes, as they detects and correct errors on the symbol level.

Decoding Full-Length Message CCSDS RS Codes

Like encoding, decoding of CCSDS RS codes is also done row-wise. The input vector length is a product of interleaving depth (i) and codeword length (n). n is fixed to 255 symbols according to CCSDS 131.0-B-3 Section 4 [1]. The input vector is composed of message and parity symbols.

Decoding Shortened Message CCSDS RS Codes

Like encoding, the decoding of CCSDS RS codes is also done row-wise. The input vector length is a product of the interleaving depth (i) and the value calculated by n-k+s. The input vector is composed of shortened message and parity symbols.

References

[1] TM Synchronization and Channel Coding. Recommendation for Space Data System Standards. CCSDS 131.0-B-3. Blue Book. Issue 3. Washington, D.C.: CCSDS, September 2017.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

Version History

Introduced in R2021a

R2024b: Support for any interleaving depth

Interleaving depth i now supports any positive value.