tpcenc

Turbo product code (TPC) encoder

Syntax

code = tpcenc(msg,N,K)

code = tpcenc(msg,N,K,S)

Description

code = tpcenc(msg,N,K) performs 2-D TPC encoding of the input message, msg, using two linear block codes specified by codeword length N and message length K. For a description of 2-D TPC encoding, see Turbo Product Code Construction.

code = tpcenc(msg,N,K,S) performs 2-D TPC encoding on the shortened input message of length S, using a 2-D TPC encoder specified by codeword length (N–K+S) and message length S.

Examples

Encode Using Full-Length TPC Codes

Encode a random bit vector using 2-D turbo product coding (TPC) with extended Hamming codes and extended BCH codes.

Specify (N,K) code pairs for TPC encoding.

N = [32;64]; 
K = [21;57]; 

Generate a column vector of random message bits. The desired length for the message bits is the product of elements in K.

msg = randi([0 1],prod(K),1);

TPC-encode the message.

code = tpcenc(msg,N,K);

Verify that the length of the encoded codeword is the product of elements in N.

size(code)

ans = 1×2

        2048           1

prod(N)

ans = 2048

Encode Shortened Message Using Turbo Product Coding

Encode a random bit vector using 2-D turbo product coding (TPC), applying message shortening.

Specify (N,K) code pairs and S for TPC encoding.

N = [32;64];
K = [21;57];
S = [19;24];

Generate a column vector of random message bits. The desired length for the shortened message bits is the product of the elements in S.

msg = randi([0 1],prod(S),1);

TPC-encode the shortened message.

code = tpcenc(msg,N,K,S);

Verify that the length of the encoded codeword is the product of elements in (N-K+S).

size(code)

ans = 1×2

   930     1

prod(N-K+S)

ans = 930

Input Arguments

msg — Input message bits to encode

column vector

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

• For a full-length input messages, the length of the column vector must be the product of the elements in K.

• For a shortened input messages, the length of the column vector must be the product of the elements in S.

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

N — Codeword length

two-element integer vector

Codeword length, specified as a two-element integer vector, [N_R; N_C]. N_R represents the number of rows in the product code matrix. N_C represents the number of columns in the product code matrix. For more information about N_R and N_C, see Turbo Product Code Construction. For a list of valid (N(i),K(i)) code pairs, see Component Codes.

Data Types: double

K — Message length

two-element integer vector

Message length, specified as a two-element integer vector, [K_R; K_C]. For a full-length message, the input column vector containing the message bits to encode is arranged into a K_R-by-K_C matrix. K_R represents the number of rows in the message matrix. K_C represents the number of columns in the message matrix. For more information about K_R and K_C, see Turbo Product Code Construction. For a list of valid (N(i),K(i)) code pairs, see Component Codes.

Data Types: double

S — Shortened message length

two-element integer vector

Shortened message length, specified as a two-element integer vector, [S_R; S_C]. For a shortened message, the input column vector containing the message bits to encode is arranged into an S_R-by-S_C matrix. S_R represents the number of rows in the matrix. S_C represents the number of columns in the matrix. For more information about S_R and S_C, see Turbo Product Code Construction.

When you specify this parameter, specify N and K vectors for the full-length TPC codes that are shortened to (N(i)–K(i)+S(i), S(i)) codes.

Data Types: double

Output Arguments

code — TPC-encoded message

column vector

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

• For full-length input messages, the length of the returned column vector is the product of the elements in N.

• For shortened input messages, the length of the returned column vector is the product of the elements in (N–K+S).

More About

Component Codes

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. Volume 46, Number 8, August 1998, pp. 1003–1010.

Extended Capabilities

C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

• TPC parameters N, K, and S must be constant values. If the value used for each of these parameters does not change, then you can assign them by expression or variable.

Version History

Introduced in R2018a