Decode convolutionally encoded data using Viterbi algorithm
Convolutional sublibrary of Error Detection and Correction
The Viterbi Decoder block decodes input symbols to produce binary output symbols. This block can process several symbols at a time for faster performance.
This block can output sequences that vary in length during simulation. For more information about sequences that vary in length, or variablesize signals, see VariableSize Signal Basics (Simulink) in the Simulink^{®} documentation.
If the convolutional code uses an alphabet of 2^{n} possible symbols, this block's input vector length is L*n for some positive integer L. Similarly, if the decoded data uses an alphabet of 2^{k} possible output symbols, this block's output vector length is L*k.
This block accepts a column vector input signal with any positive integer value for L. For variablesized inputs, the L can vary during simulation. The operation of the block is governed by the operation mode parameter."
For information about the data types each block port supports, see the Supported Data Types table on this page.
The entries of the input vector are either bipolar, binary, or integer data, depending on the Decision type parameter.
Decision type Parameter  Possible Entries in Decoder Input  Interpretation of Values  Branch metric calculation 

 Real numbers  Positive real: logical zero Negative real: logical one  Euclidean distance 
 0, 1  0: logical zero 1: logical one  Hamming distance 
 Integers between 0 and 2^{b}1, where b is the Number of soft decision bits parameter.  0: most confident decision for logical zero 2^{b}1: most confident decision for logical one Other values represent less confident decisions.  Hamming distance 
To illustrate the soft decision situation more explicitly, the following table lists interpretations of values for 3bit soft decisions.
Input Value  Interpretation 

0  Most confident zero 
1  Second most confident zero 
2  Third most confident zero 
3  Least confident zero 
4  Least confident one 
5  Third most confident one 
6  Second most confident one 
7  Most confident one 
The Viterbi decoder block has three possible methods for transitioning between successive input frames. The Operation mode parameter controls which method the block uses:
In Continuous
mode, the
block saves its internal state metric at the end of each input, for
use with the next frame. Each traceback path is treated independently.
In Truncated
mode, the
block treats each input independently. The traceback path starts at
the state with the best metric and always ends in the allzeros state.
This mode is appropriate when the corresponding Convolutional Encoder
block has its Operation mode set to Truncated
(reset every frame)
.
In Terminated
mode, the
block treats each input independently, and the traceback path always
starts and ends in the allzeros state. This mode is appropriate when
the uncoded message signal (that is, the input to the corresponding
Convolutional Encoder block) has enough zeros at the end of each input
to fill all memory registers of the feedforward encoder. If the encoder
has k
input streams and constraint length vector constr
(using
the polynomial description), "enough" means k*max(constr1)
.
For feedback encoders, this mode is appropriate if the corresponding
Convolutional Encoder block has Operation mode set
to Terminate trellis by appending bits
.
Note:
When this block outputs sequences that vary in length during
simulation and you set the Operation mode to 
Use the Continuous
mode when the
input signal contains only one symbol.
The Traceback depth parameter, D, influences the decoding delay. The decoding delay is the number of zero symbols that precede the first decoded symbol in the output.
If you set the Operation mode to Continuous
,
the decoding delay consists of D zero symbols
If the Operation mode parameter
is set to Truncated
or Terminated
,
there is no output delay and the Traceback depth parameter
must be less than or equal to the number of symbols in each input.
As a general estimate, the Traceback depth value is approximately two to three times (k – 1)/(1 – r), where k is the constraint length of the code and r is the code rate [7]. For example:
A rate 1/2
code has a Traceback
depth of 5(k –
1).
A rate 2/3
code has a Traceback
depth of 7.5(k –
1).
A rate 3/4
code has a Traceback
depth of 10(k –
1).
A rate 5/6
code has a Traceback
depth of 15(k –
1).
The reset port is usable only when the Operation mode parameter
is set to Continuous
. Selecting Enable
reset input port gives the block an additional input port,
labeled Rst
. When the Rst
input
is nonzero, the decoder returns to its initial state by configuring
its internal memory as follows:
Sets the allzeros state metric to zero.
Sets all other state metrics to the maximum value.
Sets the traceback memory to zero.
Using a reset port on this block is analogous to setting Operation
mode in the Convolutional Encoder block
to Reset on nonzero input via port
.
The reset port supports double
or boolean
typed
signals.
There are three main components to the Viterbi decoding algorithm. They are branch metric computation (BMC), addcompare and select (ACS), and traceback decoding (TBD). The following diagram illustrates the signal flow for a k/n rate code.
As an example of a BMC diagram, a 1/2 rate, nsdec = 3 signal flow would be as follows.
$$\begin{array}{c}WL=nsdec+n1\\ n=2\Rightarrow WL=4\end{array}$$
The ACS component is generally illustrated as shown in the following diagram.
Where WL2
is specified on the
mask by the user.
In the flow diagrams above, inNT, bMetNT , stMetNT, and outNT
are numerictype
(FixedPoint Designer) objects,
and bMetFIMATH and stMetFIMATH, are fimath (FixedPoint Designer)
objects.
For some commonly used puncture patterns for specific rates and polynomials, see the last three references.
The following two example models showcase the fixedpoint Viterbi decoder block used for both hard and softdecision convolutional decoding.
If you are reading this reference page in the MATLAB^{®} Help
Browser, click Fixedpoint
HardDecision Viterbi Decoding and Fixedpoint SoftDecision Viterbi
Decoding to open the models. These can also be found as doc_fixpt_vitharddec.mdl
and doc_fixpt_vitsoftdec.mdl
under help\toolbox\commm\examples
.
The layout of the soft decision model
example is also similar to the existing doc example on SoftDecision Decoding, which
can be found at help\toolbox\comm\examples\doc_softdecision.mdl
The purpose of this model is to highlight the fixedpoint modeling attributes of the Viterbi decoder, using a familiar layout.
The two simulations have a similar structure and have most parameters in common. A data source produces a random binary sequence that is convolutionally encoded, BPSK modulated, and passed through an AWGN channel.
The Convolutional encoder is configured as a rate 1/2 encoder. For every 2 bits, the encoder adds another 2 redundant bits. To accommodate this, and add the correct amount of noise, the Eb/No (dB) parameter of the AWGN block is in effect halved by subtracting 10*log10(2).
For the harddecision case, the BPSK demodulator produces hard decisions, at the receiver, which are passed onto the decoder.
For the softdecision case, the BPSK demodulator produces soft decisions, at the receiver, using the loglikelihood ratio. These soft outputs are 3bit quantized and passed onto the decoder.
After the decoding, the simulation compares the received decoded symbols with the original transmitted symbols in order to compute the bit error rate. The simulation ends after processing 100 bit errors or 1e6 bits, whichever comes first.
Fixedpoint modeling enables bittrue simulations which take into account hardware implementation considerations and the dynamic range of the data/parameters. For example, if the target hardware is a DSP microprocessor, some of the possible word lengths are 8, 16, or 32 bits, whereas if the target hardware is an ASIC or FPGA, there may be more flexibility in the word length selection.
To enable fixedpoint Viterbi decoding, the block input must be of type ufix1 (unsigned integer of word length 1) for hard decisions. Based on this input (either a 0 or a 1), the internal branch metrics are calculated using an unsigned integer of word length = (number of output bits), as specified by the trellis structure (which equals 2 for the harddecision example).
For soft decisions, the block input must be of type ufixN (unsigned integer of word length N), where N is the number of softdecision bits, to enable fixedpoint decoding. The block inputs must be integers in the range 0 to 2^{N1}. The internal branch metrics are calculated using an unsigned integer of word length = (N + number of output bits  1), as specified by the trellis structure (which equals 4 for the softdecision example).
The State metric word length is specified by the user and usually must be greater than the branch metric word length already calculated. You can tune this to be the most suitable value (based on hardware and/or data considerations) by reviewing the logged data for the system.
Enable the logging by selecting Analysis > FixedPoint
Tool. In the FixedPoint Setting GUI, set the Fixedpoint
instruments mode to Minimums, maximums and overflows
,
and rerun the simulation. If you see overflows, it implies the data
did not fit in the selected container. You could either increase the
size of the word length (if your hardware allows it) or try scaling
the data prior to processing it. Based on the minimum and maximum
values of the data, you are also able to determine whether the selected
container is of the appropriate size.
Try running simulations with different values of State metric word length to get an idea of its effect on the algorithm. You should be able to narrow down the parameter to a suitable value that has no adverse effect on the BER results.
To run the same model with double precision data, Select Analysis
> FixedPoint Tool. In the FixedPoint Tool GUI,
select the Data type override to be Double
.
This selection overrides all data type settings in all the blocks
to use double precision. For the Viterbi Decoder block,
as Output type was set to Boolean
,
this parameter should also be set to double.
Upon simulating the model, note that the doubleprecision and fixedpoint BER results are the same. They are the same because the fixedpoint parameters for the model have been selected to avoid any loss of precision while still being most efficient.
The two models are set up to run from within BERTool to generate a simulation curve that compares the BER performance for harddecision versus softdecision decoding.
To generate simulation results for doc_fixpt_vitharddec.mdl
,
do the following:
Type bertool
at the MATLAB command
prompt.
Go to the Monte Carlo pane.
Set the Eb/No range to 2:5
.
Set the Simulation model to doc_fixpt_vitharddec.mdl
.
Make sure that the model is on path.
Set the BER variable name to BER
.
Set the Number of errors to 100
,
and the Number of bits to 1e6
.
Press Run and a plot generates.
To generate simulation results for doc_fixpt_vitsoftdec.mdl
,
just change the Simulation model in step 4 and
press Run.
Notice that, as expected, 3bit softdecision decoding is better than harddecision decoding, roughly to the tune of 1.7 dB, and not 2 dB as commonly cited. The difference in the expected results could be attributed to the imperfect quantization of the soft outputs from the demodulator.
MATLAB structure that contains the trellis description of the convolutional encoder. Use the same value here and in the corresponding Convolutional Encoder block.
Select this check box to specify a punctured input code. The field, Punctured code, appears.
Constant puncture pattern vector used at the transmitter (encoder).
The puncture vector is a pattern of 1
s and 0
s.
The 0
s indicate the punctured bits. When you select Punctured
code, the Punctured vector field appears.
When you check this box, the decoder opens an input port labeled Era
.
Through this port, you can specify an erasure vector pattern of 1
s
and 0
s, where the 1
s indicate
the erased bits.
For these erasures in the incoming data stream, the decoder
does not update the branch metric. The widths and the sample times
of the erasure and the input data ports must be the same. The erasure
input port can be of data type double
or Boolean
.
Specifies the use of Unquantized
, Hard
Decision
, or Soft Decision
for
the branch metric calculation.
Unquantized
decision uses
the Euclidean distance to calculate the branch metrics.
Soft Decision
and Hard
Decision
use the Hamming distance to calculate the branch
metrics, where Number of soft decision bits equals 1
.
The number of soft decision bits to represent each input. This
field is active only when Decision type is set
to Soft Decision
.
Select this check box to throw an error when quantized input
values are out of range. This check box is active only when Decision
type is set to Soft Decision
or Hard
Decision
.
The number of trellis branches to construct each traceback path.
Method for transitioning between successive input frames: Continuous
, Terminated
,
and Truncated
.
Note:
When this block outputs sequences that vary in length during
simulation and you set the Operation mode to 
When you check this box, the decoder opens an input port labeled Rst
.
Providing a nonzero input value to this port causes the block to set
its internal memory to the initial state before processing the input
data.
When you select this option, the Viterbi Decoder block resets
after decoding the encoded data. This option is available only when
you set Operation mode to Continuous
and
select Enable reset input port. You must enable
this option for HDL support.
The output signal's data type can be double
, single
, boolean
, int8
, uint8
, int16
, uint16
, int32
, uint32
,
or set to 'Inherit via internal rule'
or 'Smallest
unsigned integer'
.
When set to 'Smallest unsigned integer'
,
the output data type is selected based on the settings used in the Hardware
Implementation pane of the Configuration Parameters dialog
box of the model. If ASIC/FPGA
is selected in the Hardware
Implementation pane, the output data type is ufix(1)
.
For all other selections, it is an unsigned integer with the smallest
specified wordlength corresponding to the char value (e.g., uint8
).
When set to 'Inherit via internal rule'
(the
default setting), the block selects doubletyped outputs for double
inputs, singletyped outputs for single inputs, and behaves similarly
to the 'Smallest unsigned integer'
option for all
other typed inputs.
Port  Supported Data Types 

Input 

Output 

This block supports HDL code generation using HDL Coder™. HDL Coder provides additional configuration options that affect HDL implementation and synthesized logic. For more information on implementations, properties, and restrictions for HDL code generation, see Viterbi Decoder in the HDL Coder documentation.
[1] Clark, G. C. Jr. and J. Bibb Cain., ErrorCorrection Coding for Digital Communications, New York, Plenum Press, 1981.
[2] Gitlin, R. D., J. F. Hayes, and S. B. Weinstein, Data Communications Principles, New York, Plenum, 1992.
[3] Heller, J. A. and I. M. Jacobs, "Viterbi Decoding for Satellite and Space Communication," IEEE Transactions on Communication Technology, Vol. COM19, October 1971, pp 835–848.
[4] Yasuda, Y., et. al., "Highrate punctured convolutional codes for soft decision Viterbi decoding," IEEE Transactions on Communications, Vol. COM32, No. 3, pp 315–319, March 1984.
[5] Haccoun, D., and Begin, G., "Highrate punctured convolutional codes for Viterbi and sequential decoding," IEEE Transactions on Communications, Vol. 37, No. 11, pp 1113–1125, Nov. 1989.
[6] Begin, G., et.al., "Further results on highrate punctured convolutional codes for Viterbi and sequential decoding," IEEE Transactions on Communications, Vol. 38, No. 11, pp 1922–1928, Nov. 1990.
[7] Moision, B., "A Truncation Depth Rule of Thumb for Convolutional Codes," Information Theory and Applications Workshop, pp. 555–557, 2008.