LDPC Encoder

Encode binary low-density parity-check (LDPC) code

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Libraries:
Communications Toolbox / Error Detection and Correction / Block

Description

The LDPC Encoder block applies LDPC coding to a binary input message. LDPC codes are linear error control codes with sparse parity-check matrices and long block lengths that can attain performance near the Shannon limit.

The input and output are discrete-time signals. The ratio of the output sample time to the input sample time is K/N, where:

• N is the length of the received signal and must be in the range (0, 2³¹).

• K is the length of the uncoded message and must be less than N.

Examples

LDPC Encode and Decode QPSK-Modulated Signal in Simulink

Transmit an LDPC-encoded, QPSK-modulated bit stream through an AWGN channel. Demodulate and decode the received signal. Compute the error statistics.

Open Model

DVB-S.2 Link, Including LDPC Coding in Simulink

The state-of-the-art channel coding scheme used in the second generation Digital Video Broadcasting standard (DVB-S.2), which is deployed by DIRECTV in the United States. The coding scheme is based on concatenation of LDPC (Low-Density Parity-Check) and BCH codes. LDPC codes, invented by Gallager in his seminal doctoral thesis in 1960, can achieve extremely low error rates near channel capacity by using a low-complexity iterative decoding algorithm. The outer BCH codes are used to correct sporadic errors made by the LDPC decoder.

Open Model

Ports

Input

In — Input message

binary column vector

Input message, specified as a K-by-1 column vector containing binary-valued elements. K is the length of the uncoded message.

Data Types: double | Boolean

Output

Out — LDPC codeword

column vector

LDPC codeword, returned as an N-by-1 column vector. N is the number of bits in the LDPC codeword. The output signal inherits its data type from the input signal. The LDPC codeword output is a solution to the parity-check equation. The input message comprises the first K bits of the LDPC codeword output, and the parity check comprises the remaining (N – K) bits.

Data Types: double | Boolean

Parameters

Parity-check matrix (sparse binary (N-K)-by-N matrix) — Parity-check matrix

dvbs2ldpc(1/2) (default) | sparse binary matrix | nonsparse index matrix

Parity-check matrix, specified as a sparse (N – K)-by-N binary-valued matrix. N is the length of the output LDPC codeword and must be in the range (0, 2³¹). K is the length of the uncoded message and must be less than N. The last (N – K) columns in the parity-check matrix must be an invertible matrix in the Galois field of order 2, gf(2).

You can also specify the parity-check matrix as a two-column nonsparse index matrix, I, that defines the row and column indices of the 1s in the parity-check matrix such that sparse(I(:,1),I(:,2),1).

This parameter accepts numeric data types. When you set this parameter to a sparse binary matrix, this parameter also accepts the Boolean data type.

The default value uses the dvbs2ldpc function to configure a sparse parity-check matrix for half-rate LDPC coding, as specified in the DVB-S.2 standard.

Note

• When the last (N – K) columns of the parity-check matrix form a triangular matrix, forward or backward substitution is performed to solve the parity-check equation.

• When the last (N – K) columns of the parity-check matrix do not form a triangular matrix, a matrix inversion is performed to solve the parity-check equation. If a large matrix needs to be inverted, initializations or updates take more time.

Example: dvbs2ldpc(R,'indices') configures the index matrix for the DVB-S.2 standard, where R is the code rate, and 'indices' specifies the output format of dvbs2ldpc as a two-column double-precision matrix that defines the row and column indices of the 1s in the parity-check matrix.

Block Characteristics

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

Extended Capabilities

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

Version History

Introduced in R2007a