Engee documentation

Viterbi Decoder

Decoding convolutionally encoded data using the Viterbi algorithm.

viterbi decoder

Description

The Viterbi Decoder block decodes the input symbols obtained by convolutional coding to produce binary output symbols using the Viterbi algorithm. The lattice structure defines the convolutional coding scheme.

Ports

Input

Port_1 - input word obtained by convolutional coding
`vector-column

The input word received by convolutional coding, specified as a column vector. If the decoder accepts input bitstreams (that is, it can accept possible input symbols), the length of the input block vector is equal to for some positive integer .

For more information, see Input and output data sizes, Input data and solution type, and the description of the Operation mode parameter.

Data types: Float32, Float64, Int8, Int16, Int32, UInt8, UInt16, UInt32, Bool.

Output

Port_1 - output message
binary vector-column

Output message returned as a binary vector-column. If the decoder outputs output bitstreams (that is, it can output possible output symbols), the length of the block output vector is equal to for some positive integer .

For more information, see Input and Output Dimensions.

Data types: Float32, Float64, Int8, Int16, Int32, UInt8, UInt16, UInt32, Bool.

Parameters

Encoded data parameters

Trellis structure - description of convolutional code through code lattice
poly2trellis(7, [171 133]) (by default)

A lattice description of a convolutional code given as a lattice structure for code with rate , where is the number of input bitstreams and is the number of output bitstreams.

To create the lattice structure you can use the poly2trellis function or set it manually.

The lattice structure contains the following fields:

  • numInputSymbols - the number of symbols coming to the input of the encoder, set as an integer equal to , where K is the number of input bit streams.

  • numOutputSymbols - the number of symbols arriving at the output of the encoder is set as an integer equal to , where K is the number of output bit streams.

  • numStates - number of states in the encoding device, specified as degree 2.

  • nextStates - the next states for all combinations of current states and current inputs, given as a matrix of integers. The size of the matrix must be numStates at .

  • outputs - outputs for all combinations of current states and current inputs, given as a matrix of octal numbers. The matrix size should be numStates at .

Branch metric computation parameters

Decision type - decoder decision type
Hard decision (by default) | Unquantized

Decision type of decoder, options to select:

  • Hard decision - the decoder uses the Hemming distance to compute the branching metric. The input must be a vector of hard decision values that represent 0 or 1. The data type of the input must be double precision, single precision, logical or numeric.

  • Unquantised - the decoder uses Euclidean distance to compute the branching metric. The input data must be a vector of real values of double or single precision, unquantised. The object converts positive values to logical ones and negative values to logical zeros.

Traceback decoding parameters

Traceback depth - traceback depth
34 (By default) | positive integer

The traceback depth is specified as an integer that indicates the number of grid branches used to build each traceback path.

The trace depth affects the decoding delay. The decode delay is the number of zero characters that precede the first decoded character in the output.

In continuous mode operation, the decoding delay is equal to the number of trace depth characters.

It is generally estimated that a typical trace depth value is about two to three times , where

  • - is the length of constraints in the code;

  • ;

  • - is the number of input symbols;

  • - number of output symbols;

  • - vector of puncture patterns.

For example, if we apply this general estimate, we get these approximate trace depths:

  • A code with rate 1/2 has a trace depth of .

  • A code with speed 2/3 has a trace depth of .

  • A code with speed 3/4 has a trace depth of .

  • A 5/6 speed code has a trace depth of .

More information in 7.

Operation mode - method of termination of the encoded frame
Continuous (by default) | Truncated

The encoded frame termination method specified as one of these mode values:

  • Continuous - the block retains its internal state metric at the end of each input for use with the next frame. Each trace path is processed independently. This mode results in a decoding delay of Traceback depth zero bits for convolutional code at , where is the number of message characters and is the number of encoded characters.

  • Truncated - The block processes each input independently. The trace path starts from the state with the best metric and always ends in the all zeros state. This mode is suitable if Truncated (reset every frame) is set for the corresponding block Convolutional Encoder for the Operation mode parameter. There is no output delay in this mode.

The decoder state is reset at each input time step if the block outputs sequences whose length changes during the simulation and the Truncated operation mode is set.

If the input signal contains only one character, use the Continuous mode.

Read more

Input and output data sizes

If the convolution code uses an alphabet of possible symbols, the length of the input vector must be for some positive integer . Similarly, if the decoded data uses an alphabet of possible output symbols, the length of the output vector will be .

This block accepts the input signal as a column vector with any positive integer value for . For variable-sized input signals, can be changed during the simulation. The operation of the block is controlled by the operation mode parameter.

This table summarises the data types supported for input and output ports.

Port Supported Data Type

Input

  • Double precision floating point number.

  • Single-precision floating-point number.

  • Boolean value for `Hard decision' mode.

  • 8-, 16- and 32-bit signed integers for `Hard decision' mode.

  • 8-, 16- and 32-bit unsigned integers for `Hard decision' mode.

Output

  • Double-precision floating-point number.

  • Single-precision floating-point number.

  • Boolean value.

  • 8-, 16- and 32-bit signed integers.

  • 8-, 16- and 32-bit integers without sign.
Input data and solution type

The input vector entries are either bipolar real, binary, or integer data depending on the value of the Decision type parameter.

Decision type Possible decoder input entries Interpreting values Calculating the branching metric

Unquantised.

Real numbers.

Input values outside the range are truncated to the values and respectively.

Positive real number: logical zero.

Negative real number: logical one.

Euclidean distance

Hard Decision.

0, 1

0: logical zero.

1: logical one.

Hemming distance

Bibliography

[1] Clark, George C., and J. Bibb Cain. Error-Correction Coding for Digital Communications. Applications of Communications Theory. New York: Plenum Press, 1981.

[2] Gitlin, Richard D., Jeremiah F. Hayes, and Stephen B. Weinstein. Data Communications Principles. Applications of Communications Theory. New York: Plenum Press, 1992.

[3] Heller, J., and I. Jacobs. "Viterbi Decoding for Satellite and Space Communication." IEEE Transactions on Communication Technology 19, no. 5 (October 1971): 835-48. https://doi.org/10.1109/TCOM.1971.1090711.

[4] Yasuda, Y., K. Kashiki, and Y. Hirata. "High-Rate Punctured Convolutional Codes for Soft Decision Viterbi Decoding." IEEE Transactions on Communications 32, no. 3 (March 1984): 315-19. https://doi.org/10.1109/TCOM.1984.1096047.

[5] Haccoun, D., and G. Begin. "High-Rate Punctured Convolutional Codes for Viterbi and Sequential Decoding." IEEE Transactions on Communications 37, no. 11 (November 1989): 1113-25. https://doi.org/10.1109/26.46505.

[6] Begin, G., D. Haccoun, and C. Paquin. "Further Results on High-Rate Punctured Convolutional Codes for Viterbi and Sequential Decoding." IEEE Transactions on Communications 38, no. 11 (November 1990): 1922-28. https://doi.org/10.1109/26.61470.

[7] Moision, B. "A Truncation Depth Rule of Thumb for Convolutional Codes." In Information Theory and Applications Workshop (January 27 2008-February 1 2008, San Diego, California), 555-557. New York: IEEE, 2008.