ldpcDecoderConfig

Create LDPC decoder configuration

Since R2021b

Description

The ldpcDecoderConfig object is a configuration object for the ldpcDecode function. The object specifies the low-density parity-check (LDPC) matrix and read-only properties to provide information about the configured matrix.

Creation

Syntax

decodercfg = ldpcDecoderConfig

decodercfg = ldpcDecoderConfig(H)

decodercfg = ldpcDecoderConfig(H,alg)

decodercfg = ldpcDecoderConfig(encodercfg)

decodercfg = ldpcDecoderConfig(encodercfg,alg)

Description

decodercfg = ldpcDecoderConfig creates an LDPC decoder configuration object that specifies a rate 5/6 LDPC code from the WLAN 802.11™ standard [1].

decodercfg = ldpcDecoderConfig(H) configures the output object setting the ParityCheckMatrix property H.

decodercfg = ldpcDecoderConfig(H,alg) configures the output object setting the ParityCheckMatrix property to H and the Algorithm property to alg.

decodercfg = ldpcDecoderConfig(encodercfg) sets properties based on the input ldpcEncoderConfig configuration object, encodercfg.

decodercfg = ldpcDecoderConfig(encodercfg,alg) sets properties based on the input ldpcEncoderConfig configuration object, encodercfg, and sets the Algorithm property to alg.

Validation of the object settings is performed when the ldpcDecode function is called with the object as an input.

Properties

ParityCheckMatrix — Parity-check matrix

sparse logical 108-by-648 matrix (default) | sparse logical (N – K)-by-N matrix

Parity-check matrix, specified as a sparse logical (N – K)-by-N matrix, where N > K > 0. N is the LDPC codeword block length. K is the number of information bits in the LDPC codeword. The default is the parity-check matrix of rate 5/6 LDPC code with a block length of 648 as specified in the WLAN 802.11 standard [1]. Specifically, the default is the sparse logical 108-by-648 matrix H output by the ldpcQuasiCyclicMatrix function in this code.

P = [
 17 13  8 21  9  3 18 12 10  0  4 15 19  2  5 10 26 19 13 13  1  0 -1 -1
  3 12 11 14 11 25  5 18  0  9  2 26 26 10 24  7 14 20  4  2 -1  0  0 -1
 22 16  4  3 10 21 12  5 21 14 19  5 -1  8  5 18 11  5  5 15  0 -1  0  0
  7  7 14 14  4 16 16 24 24 10  1  7 15  6 10 26  8 18 21 14  1 -1 -1  0
 ];
blockSize = 27;
H = ldpcQuasiCyclicMatrix(blockSize,P);

Data Types: logical

Algorithm — LDPC decoding algorithm

'bp' (default) | 'layered-bp' | 'norm-min-sum' | 'offset-min-sum'

LDPC decoding algorithm, specified as one of these values:

• 'bp' — Use Belief Propagation Decoding algorithm.

• 'layered-bp' — Use Layered Belief Propagation Decoding algorithm.

• 'norm-min-sum' — Use Normalized Min-Sum Decoding algorithm.

• 'offset-min-sum' — Use Offset Min-Sum Decoding algorithm.

Data Types: char | string

BlockLength — Block length

Read-only: 648 (default) | positive scalar

This property is read-only.

Block length of the LDPC codeword (N), specified as a positive scalar. N equals the number of columns in the parity-check matrix.

Data Types: double

NumInformationBits — Number of information bits

Read-only: 540 (default) | positive scalar

This property is read-only.

Number of information bits in the LDPC codeword (K), specified as a positive scalar. K equals the number of columns of the parity-check matrix minus the number of rows of the parity-check matrix.

Data Types: double

NumParityCheckBits — Number of parity-check bits

Read-only: 108 (default) | positive scalar

This property is read-only.

Number of parity-check bits in the LDPC codeword (N – K), specified as a positive scalar. N – K equals the number of rows in the parity-check matrix.

Data Types: double

CodeRate — Code rate of LDPC code

Read-only: 5/6 (default) | positive scalar

This property is read-only.

Code rate of the LDPC code, specified as a positive scalar that is equal to NumInformationBits/BlockLength.

Data Types: double

NumRowsPerLayer — Number of rows per layer

Read-only: 108 (default) | positive scalar

This property is read-only.

Number of rows per layer, specified as a positive scalar. This property indicates the number of rows per layer when you use a layered decoding algorithm. Specifically, this property is the largest integer such that ParityCheckMatrix can be evenly split into consecutive submatrices in which at most one 1 exists in any column in any one of these submatrices.

ParityCheckMatrix(1:NumRowsPerLayer,:)

ParityCheckMatrix((NumRowsPerLayer + 1):2*NumRowsPerLayer,:)

ParityCheckMatrix((2*NumRowsPerLayer + 1):3*NumRowsPerLayer,:)

...

ParityCheckMatrix((end - NumRowsPerLayer + 1):end, :)

Dependencies

This property appears when you set the Algorithm property to 'layered-bp', 'norm-min-sum', or 'offset-min-sum'.

Data Types: double

Output Arguments

decodercfg — LDPC decoder configuration object

structure

LDPC decoder configuration object, returned as a structure.

Data Types: struct

Examples

Decode Rate 3/4 LDPC Codewords for QAM signal

Initialize parameters for the prototype matrix and block size to configure a rate 3/4 LDPC code specified in IEEE® 802.11. Create the parity-check matrix by using the ldpcQuasiCyclicMatrix function.

P = [
    16 17 22 24  9  3 14 -1  4  2  7 -1 26 -1  2 -1 21 -1  1  0 -1 -1 -1 -1
    25 12 12  3  3 26  6 21 -1 15 22 -1 15 -1  4 -1 -1 16 -1  0  0 -1 -1 -1
    25 18 26 16 22 23  9 -1  0 -1  4 -1  4 -1  8 23 11 -1 -1 -1  0  0 -1 -1
     9  7  0  1 17 -1 -1  7  3 -1  3 23 -1 16 -1 -1 21 -1  0 -1 -1  0  0 -1
    24  5 26  7  1 -1 -1 15 24 15 -1  8 -1 13 -1 13 -1 11 -1 -1 -1 -1  0  0
     2  2 19 14 24  1 15 19 -1 21 -1  2 -1 24 -1  3 -1  2  1 -1 -1 -1 -1  0
    ];
blockSize = 27;
pcmatrix = ldpcQuasiCyclicMatrix(blockSize,P);

Create LDPC encoder and decoder configuration objects, displaying their properties.

cfgLDPCEnc = ldpcEncoderConfig(pcmatrix)

cfgLDPCEnc = 
  ldpcEncoderConfig with properties:

     ParityCheckMatrix: [162×648 logical]

   Read-only properties:
           BlockLength: 648
    NumInformationBits: 486
    NumParityCheckBits: 162
              CodeRate: 0.7500

cfgLDPCDec = ldpcDecoderConfig(pcmatrix)

cfgLDPCDec = 
  ldpcDecoderConfig with properties:

     ParityCheckMatrix: [162×648 logical]
             Algorithm: 'bp'

   Read-only properties:
           BlockLength: 648
    NumInformationBits: 486
    NumParityCheckBits: 162
              CodeRate: 0.7500

Transmit an LDPC-encoded, M-QAM-modulated bit stream through an AWGN channel. Demodulate the signal, decode the received codewords, and then count bit errors. Use a for loop to process multiple SNR settings with and without LDPC forward error correction (FEC) coding of the transmitted data.

M = 64;
maxnumiter = 10;
snr = [0.5 1 1.5 2];
numframes = 20000;

for ii = 1:length(snr)
    data = randi([0 1],cfgLDPCEnc.NumInformationBits,numframes,'int8');

    % Transmit and receive with LDPC coding
    encodedData = ldpcEncode(data,cfgLDPCEnc);
    modSignal = qammod(encodedData,M,InputType='bit');
    [rxsig, noisevar] = awgn(modSignal,snr(ii));
    llrOut = qamdemod(rxsig,M, ...
        OutputType='approxllr', ... % Or use 'llr' for exact but slower LLR calculation
        NoiseVariance=noisevar);
    rxbits = ldpcDecode(llrOut,cfgLDPCDec,maxnumiter);
    fprintf(['SNR = %2.1f\n   Coded: Error rate = %1.6f, ' ...
        'Number of errors = %d\n'], ...
        snr(ii),nnz(data~=rxbits)/numel(data),nnz(data~=rxbits));

    % Transmit and receive with no LDPC coding
    noCoding = qammod(data,M,InputType='bit');
    rxNoCoding = awgn(noCoding,snr(ii));
    rxBitsNoCoding = qamdemod(rxNoCoding,M,OutputType='bit');

    fprintf(['Noncoded: Error rate = %1.6f, ' ...
        'Number of errors = %d\n\n'], ...
        nnz(data~=rxBitsNoCoding)/numel(data),nnz(data~=rxBitsNoCoding))
end

SNR = 0.5
   Coded: Error rate = 0.000441, Number of errors = 4282

Noncoded: Error rate = 0.039045, Number of errors = 379515

SNR = 1.0
   Coded: Error rate = 0.000062, Number of errors = 604

Noncoded: Error rate = 0.032813, Number of errors = 318941

SNR = 1.5
   Coded: Error rate = 0.000003, Number of errors = 27

Noncoded: Error rate = 0.027001, Number of errors = 262450

SNR = 2.0
   Coded: Error rate = 0.000000, Number of errors = 0

Noncoded: Error rate = 0.021778, Number of errors = 211686

Algorithms

LDPC decoding using one of these message-passing algorithms.

Belief Propagation Decoding

The implementation of the belief propagation algorithm is based on the decoding algorithm presented by Gallager [2].

For transmitted LDPC-encoded codeword c = c₀, c₁, …, c_n-1, the input to the LDPC decoder is the log-likelihood ratio (LLR) value $$L(c_i)=\log \left(\frac{\mathrm{Pr}(c_i=0|\text{channel output for }{c}_i)}{\mathrm{Pr}(c_i=1|\text{channel output for }{c}_i)}\right)$$.

In each iteration, the key components of the algorithm are updated based on these equations:

$$L(r_{ji})=2\text{atanh}\left({\displaystyle \prod _{i^{\prime }\in V_j\backslash i}\tanh \left(\frac{1}{2}L(q_{i^{\prime }j})\right)}\right)$$,

$$L(q_{ij})=L(c_i)+{\displaystyle \sum _{j^{\prime }\in C_i\backslash j}L(r_{j^{\prime }i})}$$, initialized as $$L(q_{ij})=L(c_i)$$ before the first iteration, and

$$L(Q_i)=L(c_i)+{\displaystyle \sum _{j^{\prime }\in C_i}L(r_{j^{\prime }i})}$$.

At the end of each iteration, L(Q_i) contains the updated estimate of the LLR value for transmitted bit c_i. The value L(Q_i) is the soft-decision output for c_i. If L(Q_i) ≤ 0, the hard-decision output for c_i is 1. Otherwise, the hard-decision output for c_i is 0.

If decoding is configured to stop when all of the parity checks are satisfied, the algorithm verifies the parity-check equation (H c' = 0) at the end of each iteration. When all of the parity checks are satisfied, or if the maximum number of iterations is reached, decoding stops.

Index sets $$C_i\backslash j$$ and $$V_j\backslash i$$ are based on the parity-check matrix (PCM). Index sets C_i and V_j correspond to all nonzero elements in column i and row j of the PCM, respectively.

This figure shows the computation of these index sets in a given PCM for i = 5 and j = 3.

To avoid infinite numbers in the algorithm equations, atanh(1) and atanh(–1) are set to 19.07 and –19.07, respectively. Due to finite precision, MATLAB^® returns 1 for tanh(19.07) and –1 for tanh(-19.07).

Layered Belief Propagation Decoding

The implementation of the layered belief propagation algorithm is based on the decoding algorithm presented in Hocevar [3], Section II.A. The decoding loop iterates over subsets of rows (layers) of the PCM. For each row, m, in a layer and each bit index, j, the implementation updates the key components of the algorithm based on these equations:

(1) $$L(q_{mj})=L(q_j)-R_{mj}$$,

(2) $$A_{mj}={\displaystyle \sum _{\begin{array}{c}n \in N\left(m\right)\\ n\ne j\end{array}}\text{ψ}(L(q_{mn}))}$$,

(3) $$s_{mj}={\displaystyle \prod _{\begin{array}{c}n \in N\left(m\right)\\ n\ne j\end{array}}\text{sign}(L(q_{mn}))}$$,

(4) $$R_{mj}=-s_{mj}\text{ψ}(A_{mj})$$, and

(5) $$L(q_j)=L(q_{mj})+R_{mj}$$.

For each layer, the decoding equation (5) works on the combined input obtained from the current LLR inputs $$L(q_{mj})$$ and the previous layer updates $$R_{mj}$$.

Because only a subset of the nodes is updated in a layer, the layered belief propagation algorithm is faster compared to the belief propagation algorithm. To achieve the same error rate as attained with belief propagation decoding, use half the number of decoding iterations when you use the layered belief propagation algorithm.

Normalized Min-Sum Decoding

The implementation of the normalized min-sum decoding algorithm follows the layered belief propagation algorithm with equation (2) replaced by

$$A_{mj}=\underset{\begin{array}{c}n \in N\left(m\right)\\ n\ne j\end{array}}{\min }(\left|L(q_{mn}) \right|\cdot \alpha )$$,

where α is in the range (0, 1] and is the scaling factor specified by the MinSumScalingFactor input argument to the ldpcDecode function. This equation is an adaptation of equation (4) presented in Chen [4].

Offset Min-Sum Decoding

The implementation of the offset min-sum decoding algorithm follows the layered belief propagation algorithm with equation (2) replaced by

$$A_{mj} = \max (\underset{\begin{array}{c}n \in N\left(m\right)\\ n\ne j\end{array}}{\min } (\left|L\left(q_{mn}\right)\right|- \beta ), 0)$$,

where β ≥ 0 and is the offset specified by the MinSumOffset input argument to the ldpcDecode function. This equation is an adaptation of equation (5) presented in Chen [4].

References

[1] IEEE^® Std 802.11-2020 (Revision of IEEE Std 802.11-2016). "Part 11: Wireless LAN Medium Access Control (MAC) and Physical Layer (PHY) Specifications." IEEE Standard for Information technology — Telecommunications and information exchange between systems. Local and metropolitan area networks — Specific requirements.

[2] Gallager, Robert G. Low-Density Parity-Check Codes. Cambridge, MA: MIT Press, 1963.

[3] Hocevar, D.E. "A reduced complexity decoder architecture via layered decoding of LDPC codes." In IEEE Workshop on Signal Processing Systems, 2004. SIPS 2004, 107-112. https://doi.org/10.1109/SIPS.2004.1363033.

[4] Chen, Jinghu, R.M. Tanner, C. Jones, and Yan Li. "Improved min-sum decoding algorithms for irregular LDPC codes." In Proceedings. International Symposium on Information Theory, 2005. ISIT 2005. https://doi.org/10.1109/ISIT.2005.1523374.

Extended Capabilities

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

Version History

Introduced in R2021b