ldpc decoder: wip

controller/fw/ldpc_decoder.c

@@ -0,0 +1,152 @@
+"""Decoding module."""
+
+/* H: decoding matrix as shape (m, n) array
+ *      m: number of equations represented by H
+ *      n: number of code words
+ * y: received message in codeword space, length n
+ *
+ * out: output array of length n where the solutions in codeword space will be written
+ *
+ * maxiter: Maximum iteration number
+ */
+int decode(uint8_t H[], const int m, n, uint8_t y[], uint8_t out[], int maxiter) {
+
+    /* fixme: preprocess the following.
+def bitsandnodes(H):
+    """Return bits and nodes of a parity-check matrix H."""
+    bits_indices, bits = scipy.sparse.find(H)[:2]
+    nodes_indices, nodes = scipy.sparse.find(H.T)[:2]
+    bits_histogram = np.bincount(bits_indices)
+    nodes_histogram = np.bincount(nodes_indices)
+    return bits_histogram, bits, nodes_histogram, nodes
+    bits_hist, bits_values, nodes_hist, nodes_values = utils.bitsandnodes(H)
+    */
+
+    float Lq[m*n];
+    float Lr[m*n];
+    float L_posteriori[n];
+
+    for (int n_iter=0; n_iter<maxiter; n_iter++) {
+        Lq, Lr, L_posteriori = inner_logbp(bits_hist, bits_values, nodes_hist,
+                                            nodes_values, y, Lq, Lr, n_iter, L_posteriori)
+        for (size_t i=0; i<n; i++)
+            out[i] = L_posteriori[i] <= 0.0f;
+
+        for (size_t i=0; i<m; i++) {
+            bool sum = 0;
+
+            for (size_t j=0; j<n; j++)
+                sum ^= H[i*n + j] * out[j];
+
+            if (sum)
+                continue;
+        }
+
+        return 1;
+    }
+    
+    return -1;
+}
+
+/* Perform inner ext LogBP solver */
+void inner_logbp(
+        size_t m, n,
+        int bits_hist[], bits_values[], nodes_hist[], nodes_values[],
+        uint8_t Lc[],
+        float Lq[], Lr[],
+        int n_iter,
+        float L_posteriori_out[]) {
+
+    /* step 1 : Horizontal */
+    int bits_counter = 0;
+    int nodes_counter = 0;
+    for (size_t i=0; i<m; i++) {
+        int ff = bits_hist[i];
+        bits_counter += ff;
+        
+        for (size_t p=bits_counter; p<bits_counter+ff; p++) {
+            int j = bits_values[p];
+
+            float x = 1;
+            if (n_iter == 0) {
+                for (size_t q=bits_counter; q<bits_counter+ff; q++) {
+                    if (bits_values[q] != j)
+                        x *= tanhf(0.5f * Lc[bits_values[q]]);
+                }
+
+            } else {
+                for (size_t q=bits_counter; q<bits_counter+ff; q++) {
+                    if (bits_values[q] != j)
+                        x *= tanhf(0.5f * Lq[i, bits_values[q]]);
+                }
+            }
+
+            float num = 1 + x;
+            float denom = 1 - x;
+            if (num == 0)
+                Lr[i*n + j] = -1.0f;
+            else if (denom == 0)
+                Lr[i*n + j] = 1.0f;
+            else
+                Lr[i*n + j] = logf(num/denom);
+        }
+    }
+
+    /* step 2 : Vertical */
+    for (size_t j=0; j<n; j++) {
+        ff = nodes_hist[j];
+
+        for (size_t p=bits_counter; p<nodes_counter+ff; p++) {
+            int i = nodes_values[p];
+
+            Lq[i, j] = Lc[j]
+
+            for (size_t q=bits_counter; q<nodes_counter+ff; q++) {
+                if (nodes_values[q] != i)
+                    Lq[i, j] += Lr[nodes_values[q], j];
+            }
+        }
+
+        nodes_counter += ff;
+    }
+
+    /* LLR a posteriori */
+    size_t nodes_counter = 0;
+    for (size_t j=0; j<n; j++) {
+        size_t ff = nodes_hist[j];
+        float sum = 0;
+        for (size_t k=bits_counter; k<nodes_counter+ff; k++)
+            sum += Lr[nodes_values[k]*n + j];
+        nodes_counter += ff;
+
+        L_posteriori_out[j] = Lc[j] + sum;
+    }
+}
+
+
+def get_message(tG, x):
+    """Compute the original `n_bits` message from a `n_code` codeword `x`.
+
+    Parameters
+    ----------
+    tG: array (n_code, n_bits) coding matrix tG.
+    x: array (n_code,) decoded codeword of length `n_code`.
+
+    Returns
+    -------
+    message: array (n_bits,). Original binary message.
+
+    """
+    n, k = tG.shape
+
+    rtG, rx = utils.gausselimination(tG, x)
+
+    message = np.zeros(k).astype(int)
+
+    message[k - 1] = rx[k - 1]
+    for i in reversed(range(k - 1)):
+        message[i] = rx[i]
+        message[i] -= utils.binaryproduct(rtG[i, list(range(i+1, k))],
+                                          message[list(range(i+1, k))])
+
+    return abs(message)