LDPC Convolutional Codes with Matlab

LDPC-CC Matlab files:

makeBaseLdpccc.m encodeLdpccc.m parityCheckMatrixHT.m minSum.m decodeLdpccc.m ldpcccBER.m

1. makeBaseLdpccc.m

This function creates LDPC-CC base matrix construction described in [1]. The function constructs N by N matrix with numOfOne ones per column or row. The next step is to add all ones column in the left, and all zeros column in the right. Figure 1. shows base matrix for N = 4 and numOfOne = 2.

Figure 1. Example of (4, 2, 2) base LDPC-CC matrix.

2. encodeLdpccc.m

This function encodes bits sequence u into time-varying LDPC convolutional codes with code rate R = 1/2. Encoder structure is shown in Figure 2.

Figure 2. Convolutional codes encoder structure.

Weight coefficients h1 is chosen from base LDPC-CC matrix derived from function 1. Weight coefficients h2 is chosen from another base matrix as shown in Figure 3.

Figure 3. Weight coefficients h1 (red and gray) and h2 (blue and gray).

From example of Figure 3. we will have h1 (start from red) = [1 1 1 0 0 0; 1 1 1 0 0 0 ; 1 1 0 0 1 0 ; 1 0 1 1 0 0] and h2 (start from blue) = [1 0 0 0 0; 1 0 0 0 0; 1 0 0 0 0; 1 0 0 0 0]. Note that h2 is smaller than h1.

Head and tail of zero bits are added to the bits sequence. (Ms + 1) head bits are used to mitigate first 'frame' error caused by nonexistent previous-period statistics, where Ms is convolutional code memory. Half of 2*(Ms + 1) tail bits are used to mitigate last 'frame' error caused by nonexistent of next-period (future) statistics. Another half of 2*(Ms + 1) are used as zero padding so that the last 'frame' is within processing (decoding) period. Lastly, T tail bits are added to flush all data from convolutional code registers, where T = convolutional code period.

The output of the function is encoded vector v which contains systematic bit information and parity bit information.

3. parityCheckMatrixHT.m

This function produces M by N of rate 1/2 H transpose parity check matrix for one decoding period based on matrix created by section 1. Figure 4. shows the example of one decoding period H transpose. All blank spaces are filled with zero.

Figure 4. H transpose matrix for decoding.

The red highlight of H transpose corresponding previous statistics, while the blue highlight corresponding to the next (future) statistics.

The input offsetV of the function determines the starting point for matrix generation. The function will then pass the new starting point (nextOffsetV) for the next decoding period.

4. minSum.m

Message passing LDPC codes decoding bases on min-sum algorithms. The corresponding H transpose in section 3. is used for decoding. The decoder will only update statistics corresponding to the non-highlighted section of H transpose.

5. decodeLdpccc.m

This function manages data flow between sub-decoder (min-sum decoder) period and between iterations. The final result is the estimate v (vHat) vector.

Within one iteration, sub-decoder hops from one decoding period of 2*(Ms + 1) to the next decoding period until all 'frame' is decoded.

6. ldpcccBER.m

This function constructs encoder, modulation, channel and decoder of LDPC-CC. The final result is bit error rate of the corresponding Eb/N0.

Simulation results

Figure 5. Simulation results

Reference

[1] A. Jimenez Feltstrom and K. Sh. Zigangirov, “Periodic Time-Varying Convolutional Codes with Low-Density Parity-Check Matrix,” IEEE Trans. Inform. Theory, 45(5):2181-2190, Sep 1999.

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ldpc_cc.zip
(5k)
Bagawan Nugroho,
Jan 8, 2013, 7:21 PM