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comm.RSDecoder System object

Package: comm

Decode data using Reed-Solomon decoder

Description

The RSDecoder object recovers a message vector from a Reed-Solomon codeword vector. For proper decoding, the property values for this object should match the property values in the corresponding RS Encoder object.

To decode data using a Reed-Solomon decoding scheme:

  1. Define and set up your Reed-Solomon decoder object. See Construction.

  2. Call step to decode data according to the properties of comm.RSDecoder. 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.

Construction

dec = comm.RSDecoder creates a block decoder System object, dec. This object performs Reed-Solomon (RS) decoding.

dec = comm.RSDecoder(N,K) creates an RS decoder object, dec with the CodewordLength property set to N and the MessageLength property set to K.

dec = comm.RSDecoder(N,K,GP) creates an RS decoder object, dec with the CodewordLength property set to N, the MessageLength property set to K, and the GeneratorPolynomial property set to GP.

dec = comm.RSDecoder(N,K,GP,S) creates an RS decoder object, dec with the CodewordLength property set to N, the MessageLength property set to K, the GeneratorPolynomial property set to GP, and the ShortMessageLength property set to S.

dec = comm.RSDecoder(N,K,GP,S,Name,Value) creates an RS decoder object, dec with the CodewordLength property set to N, the MessageLength property set to K, the GeneratorPolynomial property set to GP, and each specified property Name set to the specified Value.

dec = comm.RSDecoder(Name,Value) creates an RS decoder object, dec, with each specified property name set to the specified value. You can specify additional name-value pair arguments in any order as (Name1,Value1,...,NameN,ValueN).

Properties

BitInput

Assume that input is bits

Specify whether the input comprises bits or integers. The default is false.

When you set this property to false, the step method input data value must be a numeric, column vector of integers. The step method outputs an encoded data output vector. The output result is a column vector of integers. Each symbol that forms the input message and output codewords is an integer between 0 and 0 and 2M – 1. These integers correspond to an element of the finite Galois field gf(2M). M is the degree of the primitive polynomial that you specify with the PrimitivePolynomialSource and PrimitivePolynomial properties.

When you set this property to true, the input value must be a numeric, column vector of bits. The encoded data output result is a column vector of bits.

CodewordLength

Codeword length

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

For a full-length RS code, the value of this property must be 2M–1, where M is an integer such that 3M 16.

MessageLength

Message length

Specify the message length as a double-precision positive integer scalar value. The default is 3.

ShortMessageLengthSource

Short message length source

Specify the source of the shortened message as  Auto or Property. When this property is set to Auto, the RS code is defined by the CodewordLength, MessageLength, GeneratorPolynomial, and PrimitivePolynomial properties.

When ShortMessageLengthSource is set to Property, you must specify the ShortMessageLength property, which is used with the other properties to define the RS code. The default is Auto.

ShortMessageLength

Shortened message length

Specify the length of the shortened message as a double-precision positive integer scalar whose value must be less than or equal to MessageLength.

When ShortMessageLength < MessageLength, the RS code is shortened. The default is 3.

GeneratorPolynomialSource

Source of generator polynomial

Specify the source of the generator polynomial as Auto or Property. The default is Auto.

When you set this property to Auto, the object chooses the generator polynomial automatically. The object calculates the generator polynomial based on the value of the PrimitivePolynomialSource property.

When you set this property to Auto, the object automatically chooses the generator polynomial. The object calculates the generator polynomial based on the value of the PrimitivePolynomial  property.

When you set this property to Property, you must specify a generator polynomial using the GeneratorPolynomial  property.

GeneratorPolynomial

Generator polynomial

Specify the generator polynomial for the RS code as a double-precision integer row vector or as a Galois field row vector whose entries are in the range from 0 to 2M–1 and represent a generator polynomial in descending order of powers. The length of the generator polynomial must be CodewordLength-MessageLength+1. This property applies when you set GeneratorPolynomialSource to Property.

The default is the result of rsgenpoly(7,3,[],[],'double'), which corresponds to [1 3 1 2 3].

When you use this object to generate code, you must set the generator polynomial to a double-precision integer row vector.

CheckGeneratorPolynomial

Enable generator polynomial checking

Set this property to true to perform a generator polynomial check. The default is true. This check verifies that the specified generator polynomial is valid.

For larger codes, disabling the check accelerates processing time. As a best practice, perform the check at least once before setting this property to false. This property applies when you set GeneratorPolynomialSource to Property.

PrimitivePolynomialSource

Source of primitive polynomial

Specify the source of the primitive polynomial as Auto or 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)).

When you setPrimitivePolynomialSource to Property, you must specify a polynomial using PrimitivePolynomial.

PrimitivePolynomial

Primitive polynomial

Specify the primitive polynomial that defines the finite field gf(2M) corresponding to the integers that form messages and codewords. The default is the result of fliplr(de2bi(primpoly(3))), which is [1 0 1 1] or the polynomial x3+x+1. Specify this property as 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 PrimitivePolynomialSource to Property.

PuncturePatternSource

Source of puncture pattern

Specify the source of the puncture pattern as None or Property. The default is None.

If you set this property to None, the object does not apply puncturing to the code. If you set it to Property, the object punctures the code based on a puncture pattern vector specified in PuncturePattern.

PuncturePattern

Puncture pattern vector

Specify the pattern used to puncture the encoded data as a double-precision, binary column vector of length (CodewordLength-MessageLength). 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 PuncturePatternSource to Property.

ErasuresInputPort

Enable erasures input

Set this property to true to specify a vector of erasures as an input to the step method. The default is false. The erasures input must be a double-precision or logical binary column vector that indicates which symbols of the input codewords to erase.

The length of the erasures vector is explained in Input and Output Signal Lengths in BCH and RS System Objects.

When this property is set to false, the object assumes no erasures.

NumCorrectedErrorsOutputPort

Enable number of corrected errors output

Set this property to true to obtain the number of corrected errors as an output to the step method. The default is true. A nonnegative value in the i-th element of the error output vector, denotes the number of corrected errors in the i-th input codeword. A value of -1 in the i-th element of the error output vector indicates that a decoding error occurred for that codeword. A decoding error occurs when an input codeword has more errors than the error correction capability of the RS code.

OutputDataType

Data type of output

Specify the output data type as Same as input, double, or logical. The default is Same as input. This property applies when you set BitInput to true.

Methods

cloneCreate RS decoder object with same property values
getNumInputsNumber of expected inputs to step method
getNumOutputsNumber of outputs from step method
isLockedLocked status for input attributes and nontunable properties
releaseAllow property value and input characteristics changes
stepDecode data using a Reed-Solomon decoder

Examples

expand all

Transmit an RS-encoded, 8-DPSK-modulated symbol stream through an AWGN channel. Then, demodulate, decode, and count errors.

    enc = comm.RSEncoder;
    mod = comm.DPSKModulator('BitInput',false);
    chan = comm.AWGNChannel(...
                'NoiseMethod','Signal to noise ratio (SNR)','SNR',10);
    demod = comm.DPSKDemodulator('BitOutput',false);
    hDdecec = comm.RSDecoder;
    errorRate = comm.ErrorRate('ComputationDelay',3);

    for counter = 1:20
      data = randi([0 7], 30, 1);
      encodedData = step(enc, data);
      modSignal = step(mod, encodedData);
      receivedSignal = step(chan, modSignal);
      demodSignal = step(demod, receivedSignal);
      receivedSymbols = step(hDdecec, demodSignal);
      errorStats = step(errorRate, data, receivedSymbols);
    end

  fprintf('Error rate = %f\nNumber of errors = %d\n', ...
      errorStats(1), errorStats(2))
Error rate = 0.115578
Number of errors = 69

Transmit a shortened RS-encoded, 256-QAM-modulated symbol stream through an AWGN channel. Then demodulate, decode, and count errors.

Set the parameters for the Reed-Solomon code, where N is the codeword length, K is the nominal message length, and S is the shortened message length. Set the modulation order, M, and the number of frames, L.

N = 255;
K = 239;
S = 188;
M = 256;
L = 50;

Create the QAM modulator, QAM demodulator, AWGN channel, and error rate System objects.

mod = comm.RectangularQAMModulator(M, ...
    'NormalizationMethod','Average power');
chan = comm.AWGNChannel('NoiseMethod','Signal to noise ratio (Eb/No)', ...
    'EbNo',15,'BitsPerSymbol',log2(M));
demod = comm.RectangularQAMDemodulator(M, ...
    'NormalizationMethod','Average power');
errorRate = comm.ErrorRate('ComputationDelay',3);

Create the Reed-Solomon generator polynomial from the DVB-T standard.

gp = rsgenpoly(N,K,[],0);

Create a Reed-Solomon encoder and decoder pair using the shortened message length, S, and the DVB-T generator polynomial, gp.

enc = comm.RSEncoder(N,K,gp,S);
dec = comm.RSDecoder(N,K,gp,S);

Generate random symbol frames whose length equals one message block. Encode, modulate, apply AWGN, demodulate, decode, and collect statistics.

for counter = 1:L
    data = randi([0 1],S,log2(M));
    encodedData = step(enc,bi2de(data));
    modSignal = step(mod,encodedData);
    receivedSignal = step(chan,modSignal);
    demodSignal = step(demod,receivedSignal);
    receivedBits = step(dec,demodSignal);
    dataOut = de2bi(receivedBits);
    errorStats = step(errorRate,data(:),dataOut(:));
end

Display the error rate and number of errors.

fprintf('Error rate = %5.2e\nNumber of errors = %d\n', ...
    errorStats(1), errorStats(2))
Error rate = 2.01e-02
Number of errors = 1509

Algorithms

This object implements the algorithm, inputs, and outputs described in Algorithms for BCH and RS Errors-only Decoding.

Introduced in R2012a

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