comm.APPDecoder

Decode convolutional code by using APP method

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Description

The APPDecoder system object performs a posteriori probability (APP) decoding of a convolutional code.

To decode convolutional code by using APP method:

Create the comm.APPDecoder object and set its properties.
Call the object with arguments, as if it were a function.

To learn more about how System objects work, see What Are System Objects?.

Creation

Syntax

appDec = comm.APPDecoder

appDec = comm.APPDecoder(Name,Value)

appDec = comm.APPDecoder(trellis,Name,Value)

Description

appDec = comm.APPDecoder creates an APP decoder System object™, appDec, that decodes a convolutional code using the APP method.

example

appDec = comm.APPDecoder(Name,Value) sets properties using one or more name-value pairs. For example, comm.APPDecoder('Algorithm','True APP') configures the System object, appDec, to implement true a posteriori probability decoding. Enclose each property name in quotes.

example

appDec = comm.APPDecoder(trellis,Name,Value) creates an APP decoder object, appDec, with the TrellisStructure property set to trellis.

Properties

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Unless otherwise indicated, properties are nontunable, which means you cannot change their values after calling the object. Objects lock when you call them, and the release function unlocks them.

If a property is tunable, you can change its value at any time.

For more information on changing property values, see System Design in MATLAB Using System Objects.

`TrellisStructure` — Trellis description of constituent convolutional code
`poly2trellis(7,[171 133],171)` (default) | structure

Trellis description, specified as a MATLAB^® structure that contains the trellis description for a rate K/N code. K represents the number of input bit streams, and N represents the number of output bit streams.

You can either use the poly2trellis function to create the trellis structure or create it manually. For more about this structure, see Trellis Description of a Convolutional Code and the istrellis function.

The trellis structure contains these fields.

`numInputSymbols` — Number of symbols input to encoder
2^K

Number of symbols input to the encoder, specified as an integer equal to 2^K, where K is the number of input bit streams.

Data Types: double

`numOutputSymbols` — Number of symbols output from encoder
2^N

Number of symbols output from the encoder, specified as an integer equal to 2^N, where N is the number of output bit streams.

Data Types: double

`numStates` — Number of states in encoder
power of 2

Number of states in the encoder, specified as a power of 2.

Data Types: double

`nextStates` — Next states
matrix of integers

Next states for all combinations of current states and current inputs, specified as a matrix of integers. The matrix size must be numStates-by-2^K.

Data Types: double

`outputs` — Outputs
matrix of octal numbers

Outputs for all combinations of current states and current inputs, specified as a matrix of octal numbers. The matrix size must be numStates-by-2^K.

Data Types: double

Data Types: struct

`TerminationMethod` — Termination method of encoded frame
`'Truncated'` (default) | `'Terminated'`

Termination method of encoded frame, specified as 'Truncated' or 'Terminated'. When you set this property to 'Truncated', this System object assumes that the encoder stops after encoding the last symbol in the input frame. When you set this property to 'Terminated', this System object assumes that the encoder forces the trellis to end each frame in the all-zeros state by encoding additional symbols. If you use the comm.ConvolutionalEncoder System object to generate the encoded frame, this property value must match the property value of the convolutional encoder and this System object.

Data Types: char | string

`Algorithm` — Decoding algorithm
`'Max*'` (default) | `'True APP'` | `'Max'`

Decoding algorithm, specified as 'Max*', 'True APP', or 'Max'. When you set this property to 'True APP', this System object implements true APP decoding. When you set this property to any other value, this System object uses approximations to increase the speed of the computations. For more information, see Algorithms.

Data Types: char | string

`NumScalingBits` — Number of scaling bits
`3` (default) | integer in the range [0, 8]

Number of scaling bits, specified as an integer in the range [0, 8]. This property specifies the number of bits the decoder uses to scale the input data to avoid losing precision during the computations.

Dependencies

To enable this property, set the Algorithm property to 'Max*'.

Data Types: double

`CodedBitLLROutputPort` — Option to enable coded-bit log-likelihood ratio output
`true or 1` (default) | `false or 0`

Option to enable coded-bit log-likelihood ratio (LLR) output, specified as a numeric or logical 1 (true) or 0 (false). To disable the second output when you call this System object, set this property to 0 (false).

Data Types: logical

Usage

Syntax

[LUD,LCD] = appDec(LU,LC)

LUD = appDec(LU,LC)

Description

[LUD,LCD] = appDec(LU,LC) performs APP decoding on the sequence of LLRs of encoder input bits, LU, and the sequence of LLRs of encoded bits, LC. The System object returns LUD and LCD. These output values are the updated versions of LU and LC, respectively, and are obtained based on the encoder information.

LUD = appDec(LU,LC) performs APP decoding with the LCD output disabled. To disable the LCD output, set the CodedBitLLROutputPort property to 0 (false).

Input Arguments

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`LU` — Sequence of LLRs of encoder input data
real-valued column vector

Sequence of LLRs of encoder input data, specified as a real-valued column vector. A positive soft input is interpreted as a logical 1, and a negative soft input is interpreted as a logical 0.

Data Types: single | double

`LC` — Sequence of LLRs of encoded data
real-valued column vector

Sequence of LLRs of encoded data, specified as a real-valued column vector of. A positive soft input is interpreted as a logical 1, and a negative soft input is interpreted as a logical 0.

Data Types: single | double

Output Arguments

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`LUD` — Updated value of LU
real-valued column vector

Updated value of LU, returned as a real-valued column vector.

Data Types: single | double

`LCD` — Updated value of LC
real-valued column vector

Updated value of LC, returned as a real-valued column vector.

Data Types: single | double

Note

If the convolutional code uses an alphabet of 2ⁿ possible symbols, where n is the number of bits per input symbol, then the LC and LCD vector lengths are L × n for some positive integer L. Similarly, if the decoded data uses an alphabet of 2^k output symbols, where k is the number of bits per output symbol, then the LU and LUD vector lengths are L × k .

This System object accepts a column vector input signal with any positive integer value for L. For variable-sized inputs, L can vary during multiple calls.

Object Functions

To use an object function, specify the System object as the first input argument. For example, to release system resources of a System object named obj, use this syntax:

release(obj)

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Common to All System Objects

`step`	Run System object algorithm
`release`	Release resources and allow changes to System object property values and input characteristics
`reset`	Reset internal states of System object

Examples

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Decode Convolutional Code Using the APP Decoder

Open Live Script

Specify noise variance and the frame length in bits. Create convolutional encoder, PSK modulator, and AWGN channel System objects.

noiseVar = 2e-1;
frameLength = 300;
convEncoder = comm.ConvolutionalEncoder('TerminationMethod','Truncated');
pskMod = comm.PSKModulator('BitInput',true,'PhaseOffset',0);
awgnChan = comm.AWGNChannel('NoiseMethod','Variance', ...
    'Variance',noiseVar);

Create convolutional APP decoder, PSK demodulator, and error rate System objects.

appDecoder = comm.APPDecoder(...
    'TrellisStructure',poly2trellis(7,[171 133]), ...
    'Algorithm','True APP','CodedBitLLROutputPort',false);
pskDemod = comm.PSKDemodulator('BitOutput',true,'PhaseOffset',0, ...
    'DecisionMethod','Approximate log-likelihood ratio', ...
    'Variance',noiseVar);     
errRate = comm.ErrorRate;

Transmit a convolutionally encoded 8-PSK-modulated bit stream through an AWGN channel. Demodulate the received signal using soft-decision. Decode the demodulated signal using the APP decoder.

for counter = 1:5
     data = randi([0 1],frameLength,1);
     encodedData = convEncoder(data);
     modSignal = pskMod(encodedData);
     receivedSignal = awgnChan(modSignal);
     demodSignal = pskDemod(receivedSignal);
     % The APP decoder assumes a polarization of the soft inputs that is
     % inverse to that of the demodulator soft outputs. Change the sign of
     % demodulated signal.
     receivedSoftBits = appDecoder(zeros(frameLength,1),-demodSignal);
     % Convert from soft-decision to hard-decision.
     receivedBits = double(receivedSoftBits > 0);
     % Count errors
     errorStats = errRate(data,receivedBits);
end

Display the error rate information.

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

Error rate = 0.000000
Number of errors = 0

Algorithms

This System object implements the soft-input-soft-output APP decoding algorithm according to [1] and [2].

The 'True APP' option of the Algorithm property implements APP decoding as per the equations 20–23 in section V of [1]. To gain speed, the 'Max*' and 'Max' values of the Algorithm property approximate expressions like $\log \sum_{i} \exp (a_{i})$ by other quantities. The 'Max' option uses max(a_i) as the approximation. The 'Max*' option uses max(a_i) plus a correction term given by the expression $\ln (1 + \exp (- | a_{i - 1} - a_{i} |))$ .

Setting the Algorithm property to 'Max*' enables the NumScalingBits property of this System object. This property denotes the number of bits by which this System object scales the data it processes internally (multiplies the input by 2^{NumScalingBits} and divides the pre-output by the same factor). Use this property to avoid losing precision during computations.

References

[1] Benedetto, S., G. Montorsi, D. Divsalar, and F. Pollara. "A Soft-Input Soft-Output Maximum A Posterior (MAP) Module to Decode Parallel and Serial Concatenated Codes." Jet Propulsion Lab TDA Progress Report, 42–127, (November 1996).

[2] Viterbi, A.J. “An Intuitive Justification and a Simplified Implementation of the MAP Decoder for Convolutional Codes.” IEEE Journal on Selected Areas in Communications 16, no. 2 (February 1998): 260–64. https://doi.org/10.1109/49.661114.

[3] Benedetto, S., and G. Montorsi. “Performance of Continuous and Blockwise Decoded Turbo Codes.” IEEE Communications Letters 1, no. 3 (May 1997): 77–79. https://doi.org/10.1109/4234.585802.

Documentation

comm.APPDecoder

Description

Creation

Syntax

Description

Properties

TrellisStructure — Trellis description of constituent convolutional code poly2trellis(7,[171 133],171) (default) | structure

numInputSymbols — Number of symbols input to encoder 2K

numOutputSymbols — Number of symbols output from encoder 2N

numStates — Number of states in encoder power of 2

nextStates — Next states matrix of integers

outputs — Outputs matrix of octal numbers

TerminationMethod — Termination method of encoded frame 'Truncated' (default) | 'Terminated'

Algorithm — Decoding algorithm 'Max*' (default) | 'True APP' | 'Max'

NumScalingBits — Number of scaling bits 3 (default) | integer in the range [0, 8]

Dependencies

CodedBitLLROutputPort — Option to enable coded-bit log-likelihood ratio output true or 1 (default) | false or 0

Usage

Syntax

Description

Input Arguments

LU — Sequence of LLRs of encoder input data real-valued column vector

LC — Sequence of LLRs of encoded data real-valued column vector

Output Arguments

LUD — Updated value of LU real-valued column vector

LCD — Updated value of LC real-valued column vector

Object Functions

Common to All System Objects

Examples

Decode Convolutional Code Using the APP Decoder

Algorithms

References

Extended Capabilities

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

See Also

Functions

Objects

Blocks

Communications Toolbox Documentation

Support

`TrellisStructure` — Trellis description of constituent convolutional code
`poly2trellis(7,[171 133],171)` (default) | structure

`numInputSymbols` — Number of symbols input to encoder
2^K

`numOutputSymbols` — Number of symbols output from encoder
2^N

`numStates` — Number of states in encoder
power of 2

`nextStates` — Next states
matrix of integers

`outputs` — Outputs
matrix of octal numbers

`TerminationMethod` — Termination method of encoded frame
`'Truncated'` (default) | `'Terminated'`

`Algorithm` — Decoding algorithm
`'Max*'` (default) | `'True APP'` | `'Max'`

`NumScalingBits` — Number of scaling bits
`3` (default) | integer in the range [0, 8]

`CodedBitLLROutputPort` — Option to enable coded-bit log-likelihood ratio output
`true or 1` (default) | `false or 0`

`LU` — Sequence of LLRs of encoder input data
real-valued column vector

`LC` — Sequence of LLRs of encoded data
real-valued column vector

`LUD` — Updated value of LU
real-valued column vector

`LCD` — Updated value of LC
real-valued column vector

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