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comm.HDLRSEncoder System object

Encode data using a Reed-Solomon encoder


The HDL-optimized HDLRSEncoder System object™ creates a Reed-Solomon code with message and codeword lengths you specify.

To create a Reed-Solomon code optimized for HDL code generation:

  1. Define and set up your HDL RS encoder object. See Construction.

  2. Call step to recover a message vector from a Reed-Solomon codeword vector according to the properties of comm.HDLRSEncoder. The behavior of step is specific to each object in the toolbox.


Starting in R2016b, instead of using the step method to perform the operation defined by the System object, you can call the object with arguments, as if it were a function. For example, y = step(obj,x) and y = obj(x) perform equivalent operations.


H = comm.HDLRSEncoder returns a block encoder System object, H, that performs Reed-Solomon (RS) encoding in a streaming fashion for HDL.

H = comm.HDLRSEncoder(Name,Value,) creates an HDL-optimized block encoder System object, H, with additional options specified by one or more Name,Value pair arguments, where Name is a property name and Value is the corresponding value. Name must appear inside single quotes (''). You can specify several name-value pair arguments in any order as Name1,Value1,...,NameN,ValueN.

H = comm.HDLRSEncoder(N,K,Name,Value) creates an RS encoder object, H, with the CodewordLength property set to N, the MessageLength property set to K, and other specified property Name, Value pair arguments.



B value for polynomial generation


Source of B, the starting power for roots of the primitive polynomial

Specify the source of the B value as one of these values:

  • Auto: B=0

  • Property

Default: Auto


Codeword length

Specify the codeword length of the RS code as a double-precision, positive, integer scalar value. The default is 7.

If you set the PrimitivePolynomialSource property to Auto, CodewordLength must be in the range 3 < CodewordLength 216–1.

When you set the PrimitivePolynomialSource property to Property, CodewordLength must be in the range 3 CodewordLength 2M–1. M is the degree of the primitive polynomial that you specify with the PrimitivePolynomialSource and PrimitivePolynomial properties. M must be in the range 3 M 16. The difference (CodewordLengthMessageLength) must be an even integer. The value of this property is rounded up to 2M–1.

If the value of this property is less than 2M–1, the object assumes a shortened RS code.


Message length

Specify the message length as a double-precision, positive integer scalar value. The default is 3. The difference (CodewordLengthMessageLength) must be an even integer.


Source of primitive polynomial

Specify the source of the primitive polynomial as Auto | Property. The default is Auto.

When you set this property to Auto, the object uses a primitive polynomial of degree M = ceil(log2(CodewordLength+1)), which is the result of fliplr(de2bi(primpoly(M))).

When you set this property to Property, you can specify a polynomial using the PrimitivePolynomial property.


Primitive polynomial

Specify the primitive polynomial that defines the finite field GF(2M) corresponding to the integers that form messages and codewords. You must set this property to a double-precision, binary row vector that represents a primitive polynomial over GF(2) of degree M in descending order of powers.

This property applies when you set the PrimitivePolynomialSource property to Property.


Source of puncture pattern

Specify the source of the puncture pattern as None | Property. The default is None. If you set this property to None then the object does not apply puncturing to the code. If you set this property to Property then the object punctures the code based on a puncture pattern vector specified in the PuncturePattern property.


Puncture pattern vector

Specify the pattern used to puncture the encoded data as a double-precision, binary column vector with a length of (CodewordLengthMessageLength). The default is [ones(2,1); zeros(2,1)]. Zeros in the puncture pattern vector indicate the position of the parity symbols that are punctured or excluded from each codeword. This property applies when you set the PuncturePatternSource property to Property.


stepPerform Reed-Solomon encoding
Common to All System Objects

Create System object with same property values


Expected number of inputs to a System object


Expected number of outputs of a System object


Check locked states of a System object (logical)


Allow System object property value changes


expand all

Create an HDLRSEncoder object with RS(255,239) code. This is the code used in the IEEE802.16 Broadband Wireless Access standard.

B is the starting power of the roots of the primitive polynomial.

rsEnc = comm.HDLRSEncoder(255,239,'BSource','Property','B',0)
rsEnc = 
  comm.HDLRSEncoder with properties:

               CodewordLength: 255
                MessageLength: 239
    PrimitivePolynomialSource: 'Auto'
        PuncturePatternSource: 'None'
                      BSource: 'Property'
                            B: 0

Create a random message to encode. This message is smaller than the codeword length to demonstrate the shortened-code capability of the objects. Pad the message with zeros to accommodate the Chien search in the decoder and the decoder latency.

Note: This object syntax runs only in R2016b or later. If you are using an earlier release, replace each call of an object with the equivalent step syntax. For example, replace myObject(x) with step(myObject,x).

messageLength = 188;
dataIn = [randi([0,255],1,messageLength,'uint8') zeros(1,1024-messageLength)];
for ii = 1:1024
    messageStart = (ii==1);
    messageEnd   = (ii==messageLength);
    validIn      = (ii<=messageLength);
    [encOut(ii),startOut(ii),endOut(ii),validOut(ii)] = rsEnc(dataIn(ii),messageStart,messageEnd,validIn);

Inject errors at random locations in the encoded message. Reed-Solomon can correct up to (N-K)/2 errors in each N symbols. So, in this example the error correction capability is (255-239)/2=8 symbols.

numErrors = 8; 
loc = randperm(messageLength,numErrors);
% encOut is qualified by validOut, use an offset for injecting errors
vi = find(validOut==true,1);
for i = 1:numErrors
   idx = loc(i)+vi;
   symbol = encOut(idx);
   encOut(idx) = randi([0 255],'uint8');
   fprintf('Symbol(%d), was 0x%x now 0x%x.\n',loc(i),symbol,encOut(idx)) 
Symbol(147), was 0x1f now 0x82.
Symbol(16), was 0x6b now 0x82.
Symbol(173), was 0x3 now 0xd1.
Symbol(144), was 0x66 now 0xcb.
Symbol(90), was 0x13 now 0xa4.
Symbol(80), was 0x5a now 0x60.
Symbol(82), was 0x95 now 0xcf.
Symbol(56), was 0xf5 now 0x88.

Create an RS Decoder to detect and correct errors in the message. It must have the same code and polynomial as the encoder.

rsDec = comm.HDLRSDecoder(255,239,'BSource','Property','B',0) 
rsDec = 
  comm.HDLRSDecoder with properties:

               CodewordLength: 255
                MessageLength: 239
    PrimitivePolynomialSource: 'Auto'
                      BSource: 'Property'
                            B: 0
          NumErrorsOutputPort: false

for ii = 1:1024     
 [decOut(ii),decStartOut(ii),decEndOut(ii),decValidOut(ii),decErrOut(ii)] = rsDec(encOut(ii),startOut(ii),endOut(ii),validOut(ii));

Select the valid decoder output and compare decoded symbols to the original message.

decOut = decOut(decValidOut==1);
originalMessage = dataIn(1:messageLength);
if all(originalMessage==decOut)
    fprintf('All %d message symbols were correctly decoded.\n',messageLength)
   for jj = 1:messageLength 
      if dataIn(jj)~=decOut(jj)
        fprintf('Error in decoded symbol(%d). Original 0x%x Decoded 0x%x.\n',jj,dataIn(jj),decOut(jj))
All 188 message symbols were correctly decoded.

Extended Capabilities

Introduced in R2012b

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