# Documentation

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# comm.HDLRSDecoder System object

Decode data using a Reed-Solomon decoder

## Description

The HDL-optimized HDLRSDecoder System object™ recovers a message vector from a Reed-Solomon codeword vector. For proper decoding, the property values for this object should match those in the corresponding HDLRSEncoder System object.

To recover a message vector from a Reed-Solomon codeword vector optimized for HDL code generation:

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

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

### Note

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.

### Troubleshooting

• Each input frame must contain more than (N-K)*2 symbols, and fewer than or equal to N symbols. A shortened code is inferred when the number of valid data samples between startIn and endIn is less than N. A shortened code still requires N cycles to perform the Chien search. If the input is less than N symbols, leave a guard interval of at least N-size inactive cycles before starting the next frame.

• The decoder can operate on up to 4 messages at a time. If the object receives the start of a fifth message before completely decoding the first message, the object drops data samples from the first message. To avoid this issue, increase the number of inactive cycles between input messages.

• The generator polynomial is not specified explicitly. However, it is defined by the code word length, the message length, and the B value for the starting exponent of the roots. To get the value of B from a generator polynomial, use the genpoly2b function.

## Construction

H = comm.HDLRSDecoder creates an HDL-optimized RS decoder System object, H, that performs Reed-Solomon (RS) decoding.

H = comm.HDLRSDecoder(Name,Value) creates an HDL-optimized RS decoder 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.HDLRSDecoder(N,K,Name,Value) creates an HDL-optimized RS decoder System object, H, with the CodewordLength property set to N, the MessageLength property set to K, and other specified property names set to the specified values.

## Properties

 B B value for polynomial generation BSource 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=0Property Default: Auto CodewordLength 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 $\le$ 216–1. When you set the PrimitivePolynomialSource property to Property, CodewordLength must be in the range 3 $\le$ CodewordLength $\le$ 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$\le$ M $\le$ 16. The difference (CodewordLength –MessageLength) 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. MessageLength Message length Specify the message length as a double-precision, positive integer scalar value. The default is 3. The difference (CodewordLength – MessageLength) must be an even integer. NumErrorsOutputPort Enable number of errors output When you set this property to true, the step method outputs number of corrected errors. The number of corrected errors is not valid when errOut is asserted, since there were more errors than could be corrected. The default is false. PrimitivePolynomialSource 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. PrimitivePolynomial 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.

## Methods

 step Perform Reed-Solomon decoding
Common to All System Objects
clone

Create System object with same property values

getNumInputs

Expected number of inputs to a System object

getNumOutputs

Expected number of outputs of a System object

isLocked

Check locked states of a System object (logical)

release

Allow System object property value changes

## Examples

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);
end

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))
end
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));
end

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)
else
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))
end
end
end
All 188 message symbols were correctly decoded.