TPC Encoder

Turbo product code (TPC) encoder

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Libraries:
Communications Toolbox / Error Detection and Correction / Block

Description

The TPC Encoder block performs 2-D turbo product code (TPC) encoding of an input message. The product code is a 2-D concatenation of linear block codes. The linear block codes can be a parity check code, a Hamming code, or a BCH code capable of correcting two errors. Extended and shortened codes can be applied independently on each dimension. For a description of 2-D TPC encoding, see Turbo Product Code Construction.

For information about valid code pairs and the error-correcting capability for each valid code pair, see Component Code Pairs.

Examples

Turbo Product Code Error Rate Calculation

Perform error rate calculations for a transmission signal that has been TPC encoded and decoded.

A random signal is TPC encoded, QPSK modulated, filtered through an AWGN channel, and QPSK demodulated. The bipolar mapping is converted from negative to positive mapping and then the signal is TPC decoded. An error rate calculation compares the original message to the recovered message.

Open Example Model and Explore Its Contents

Several settings must be aligned with each other to synchronize encoding and decoding of the message. Start by deciding on a code rate, and aligning the TPC Encoder and TPC Decoder 2-D [N,K] pairs. For this example the default settings are used, [Nr,Kr] = [15,11] and [Nc,Kc] = [32,26].

The number of samples per frame and the sample time used by the Bernoulli Binary Generator block are determined based on the message length parameters, Number of rows in message, Kr and Number of columns in message, Kc.

• Number of samples per frame = (Kr*Kc) = 286

• Sample time = 1/(Kr*Kc) = 0.0035.

The white Gaussian noise the SNR setting is calculated based on the coding rate, modulation order, and Eb/N0.

• Modulation order, M = 2

• Eb/N0 = -11

• rate = (Kr*Kc)/((Nr-Kr)*(Nc-Kc)) = 14.3

• snr = 10*log10(M*rate*10^(ebn0/10)) = 3.5637

The noise variance used in the QPSK Demodulator Baseband block is calculated based on the SNR.

• Noise variance = 1/10^(snr/10) = 1/10^(3.5637/10) = 0.4402

Run the model and observe the error rate calculation. Results will vary from run to run due to the use of random input data.

Bit error rate: 0.00042

Further Exploration

To run the model yourself, open the example using the button provided or by entering open slex_tpc_err_rate_calc at the MATLAB® command prompt. Consider modifying the model to change the signal to noise ratio. When adjusting TPC Encoder settings be sure to align settings in the TPC Decoder, Bernoulli Binary Generator, AWGN Channel, and QPSK Demodulator Baseband.

Ports

Input

In — Message to encode

column vector

Input message bits to encode, specified as a column vector.

• For full-length input messages, the length of the column vector must be the product of Number of rows in message, Kr and Number of columns in message, Kc.

• For shortened input messages, the length of the column vector must be the product of Number of rows in shortened message, Sr and Number of columns in shortened message, Sc.

Data Types: single | double | int8 | int16 | int32 | uint8 | uint16 | uint32 | Boolean

Output

Out — TPC-encoded message

column vector

TPC-encoded message, returned as a column vector with the same data type as the input signal.

• For full-length input messages, the length of the column vector is the product of Number of rows in code, Nr and Number of columns in code, Nc.

• For shortened input messages, the length of the column vector is the product of (N_R–K_R+S_R) and (N_C–K_C+S_C), where:

  • N_R is the value of Number of rows in code, Nr.

  • K_R is the value of Number of rows in message, Kr.

  • S_R is the value of Number of rows in shortened message, Sr.

  • N_C is the value of Number of columns in code, Nc.

  • K_C is the value of Number of columns in message, Kc.

  • S_C is the value of Number of columns in shortened message, Sc.

Parameters

To edit block parameters interactively, use the Property Inspector. From the Simulink^® Toolstrip, on the Simulation tab, in the Prepare gallery, select Property Inspector.

Row TPC parameters

Extended codes — Extended codes indicator for TPC row parameters

on (default) | off

• When Extended codes is selected, the lists for Number of rows in code, Nr and Number of rows in message, Kr contain the valid values for extended individual code pairs (N_R,K_R).

• When Extended codes is cleared, the lists for Number of rows in code, Nr and Number of rows in message, Kr contain the valid values for nonextended individual code pairs (N_R,K_R).

Number of rows in code, Nr — Number of rows in product code matrix

16 (default) | integer

Number of rows in the product code matrix, N_R. The list of integer values varies depending on the setting for Extended codes.

Number of rows in message, Kr — Number of rows in message matrix

11 (default) | integer

Number of rows in the message matrix, K_R. The list of integer values varies depending on the setting for Extended codes and Number of rows in code, Nr.

Specify shortened message length — Specify shortened message length for rows

off (default) | on

Select Specify shortened message length to specify a value for Number of rows in shortened message, Sr.

Number of rows in shortened message, Sr — Number of rows in shortened message matrix

9 (default) | integer

Number of rows in the shortened message matrix, S_R, specified as an integer less than or equal to K_R. When you specify this parameter, provide full-length N_R and K_R values to specify the (N_R,K_R) code pair. This code pair is then shortened to the (N_R–K_R+S_R,S_R) code pair, where:

• N_R is the value of Number of rows in code, Nr.

• K_R is the value of Number of rows in message, Kr.

• S_R is the value of Number of rows in shortened message, Sr.

Dependencies

To enable this parameter, select Specify shortened message length.

Column TPC parameters

Extended codes — Extended codes indicator for TPC column parameters

on (default) | off

• When Extended codes is selected, the lists for Number of columns in code, Nc and Number of columns in message, Kc contain the valid values for extended individual code pairs (N_C,K_C).

• When Extended codes is cleared, the lists for Number of columns in code, Nc and Number of columns in message, Kc contain the valid values for nonextended individual code pairs (N_C,K_C).

Number of columns in code, Nc — Number of columns in product code matrix

32 (default) | integer

Number of columns in the product code matrix, N_C. The list of integer values varies depending on the setting for Extended codes.

Number of columns in message, Kc — Number of columns in message matrix

26 (default) | integer

Number of columns in the message matrix, K_C. The list of integer values varies depending on the setting for Extended codes and Number of columns in code, Nc.

Specify shortened message length — Specify shortened message length for columns

off (default) | on

Select Specify shortened message length to specify a value for Number of columns in shortened message, Sc.

Number of columns in shortened message, Sc — Number of columns in shortened message matrix

22 (default) | integer

Number of columns in the shortened message matrix, S_C, specified as an integer. When you specify this parameter, provide full-length N_C and K_C values to specify the (N_C,K_C) code pair. This code pair is then shortened to the (N_C–K_C+S_C, S_C) code pair, where:

• N_C is the value of Number of columns in code, Nc.

• K_C is the value of Number of columns in message, Kc.

• S_C is the value of Number of columns in shortened message, Sc.

Dependencies

To enable this parameter, select Specify shortened message length.

Simulate using — Type of simulation to run

Code generation (default) | Interpreted execution

Type of simulation to run, specified as Code generation or Interpreted execution.

• Code generation — Simulate the model by using generated C code. The first time you run a simulation, Simulink generates C code for the block. The model reuses the C code for subsequent simulations unless the model changes. This option requires additional startup time, but the speed of the subsequent simulations is faster than with the Interpreted execution option.

• Interpreted execution — Simulate the model by using the MATLAB^® interpreter. This option shortens startup time, but the speed of subsequent simulations is slower than with the Code generation option. In this mode, you can debug the source code of the block.

For more information, see Interpreted Execution vs. Code Generation (Simulink).

Block Characteristics

Data Types	Boolean | double | integer | single
Multidimensional Signals	no
Variable-Size Signals	no

More About

Component Code Pairs

This table lists the supported component code pairs for the row (N_R,K_R) and column (N_C,K_C) parameters.

• N_R and K_R represent the number of rows in the product code matrix and message matrix, respectively.

• N_C and K_C represent the number of columns in the product code matrix and message matrix, respectively.

Within each code type, any two component code pairs can form a 2-D TPC code. The table also includes the error-correction capability for each code pair.

Code type	Component Code Pairs(NR,KR) and (NC,KC)	Error-Correction Capability (T)
Hamming code	(255,247)	1
	(127,120)	1
	(63,57)	1
	(31,26)	1
	(15,11)	1
	(7,4)	1
Extended Hamming code	(256,247)	1
	(128,120)	1
	(64,57)	1
	(32,26)	1
	(16,11)	1
	(8,4)	1
BCH code	(255,239)	2
	(127,113)	2
	(63,51)	2
	(31,21)	2
	(15,7)	2
Extended BCH code	(256,239)	2
	(128,113)	2
	(64,51)	2
	(32,21)	2
	(16,7)	2
Parity check code	(256,255)	-
	(128,127)	-
	(64,63)	-
	(32,31)	-
	(16,15)	-
	(8,7)	-
	(4,3)	-

Turbo Product Code Construction

Turbo product codes (TPC) are a form of concatenated codes used as forward error-correcting (FEC) codes. Two or more component block codes, such as systematic linear block codes, are used to construct TPCs. This encoder implements 2-D product code encoding, as described in [1], using two Linear Block Codes.

The TPC encoder accepts either full-length or shortened messages.

 Construction of Full-Length Message Product Codes

Full-length input messages are encoded using specified 2-D TPC code pairs. Row-wise encoding uses the (N_C,K_C) code pair and column-wise encoding uses the (N_R,K_R) code pair. The input vector length must be K_R · K_C. The input message bits vector is arranged into a K_R-by-K_C matrix.

Row-wise encoding uses an (N_C,K_C) systematic linear block encoder with K_C bits per row. The row-wise encoding results in a K_R-by-N_C matrix that includes parity bits added to each row.

Next, column-wise encoding uses an (N_R,K_R) systematic linear block encoder on each of the N_C columns. Applying this 2-D TPC encoding to the initial K_R-by-K_C matrix results in an N_R-by-N_C matrix that includes parity bits added to each row and column.

The 2-D TPC full-code matrix is reshaped into a column vector of length N_R · N_C and returned as the TPC-encoded output.

 Construction of Shortened Message Product Codes

Shortened input messages are encoded using specified 2-D TPC code pairs. Row-wise encoding uses the (N_C,K_C) code pair and column-wise encoding uses an (N_R,K_R) code pair. The input vector length must be S_R · S_C. The input shortened message bits vector is arranged into an S_R-by-S_C matrix. The shortened message matrix prepends two dimensions by padding the beginning of the message matrix with zeros. The resulting matrix is a K_R-by-K_C matrix.

Row-wise encoding uses an (N_C,K_C) systematic linear block encoder with K_C bits per row. The row-wise encoding results in a K_R-by-N_C matrix that includes parity bits added to each row.

Next, the column-wise encoding uses an (N_R,K_R) systematic linear block encoder on each of the N_C columns.

Applying this 2-D TPC encoding to the initial K_R-by-K_C matrix and excluding the zero-padded bits from the output results in an (N_R–K_R+S_R)-by-(N_C–K_C+S_C) matrix. This matrix includes parity bits added to each row and column.

The 2-D TPC shortened-code matrix is reshaped into a column vector of length (N_R–K_R+S_R) · (N_C–K_C+S_C) and returned as the TPC-encoded output.

References

[1] Pyndiah, R. M. "Near-Optimum Decoding of Product Codes: Block Turbo Codes." IEEE Transactions on Communications. Vol. 46, Number 8, August 1998, pp. 1003–1010.

Extended Capabilities

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

Version History

Introduced in R2018b