[sparse] BCOO._dedupe moves padded indices to the front
Example:
```python
import jax.numpy as jnp
from jax.experimental import sparse

data = jnp.array([1, 1])
indices = jnp.array([1, 1])[:, None]
shape = (2,)

x = sparse.BCOO((data, indices), shape=shape)
x = x._dedupe()
print(x.data, x.indices.ravel())
# [2 0] [1 0]

x = x._dedupe()
print(x.data, x.indices.ravel())
# [0 2] [0 1]
```
The second `_dedupe()` call should leave the representation unchanged.
diff --git a/jax/experimental/sparse/bcoo.py b/jax/experimental/sparse/bcoo.py
index e21a09508..11bd06875 100644
--- a/jax/experimental/sparse/bcoo.py
+++ b/jax/experimental/sparse/bcoo.py
@@ -67,17 +67,20 @@ def _dedupe_bcoo_one(data, indices):
   if indices.shape[1] == 0:
     return data, indices
 
-  # This is a fixed-size version of jnp.unique() with return_indices=True
-  # unique values are zero-filled at the end.
-  perm = jnp.lexsort(indices.T[::-1])
+  # The following is similar to
+  #   indices_unique, inv_idx = jnp.unique(indices, axis=0, return_inverse=True,
+  #                                        size=indices.shape[0], fill_value=0)
+  # but modified to keep padding at the end of the resulting arrays.
+  is_padding = (indices == 0).all(1) & (data == 0)
+  perm = jnp.lexsort(indices[:, ::-1].T)
   aux = indices[perm]
   mask = jnp.ones(indices.shape[0], dtype=bool)
   mask = mask.at[1:].set(jnp.any(aux[1:] != aux[:-1], 1))
+  mask = mask & ~is_padding[perm]  # this is the padding modification.
   imask = jnp.cumsum(mask) - 1
   indices_unique = jnp.where(mask[:, None], aux, 0)[jnp.argsort(~mask)]
   inv_idx = jnp.zeros_like(imask).at[perm].set(imask)
 
-  # With the above, de-duping is easy.
   data_unique = jnp.zeros_like(data).at[inv_idx].add(data)
   return data_unique, indices_unique
 
diff --git a/tests/sparse_test.py b/tests/sparse_test.py
index 87e93de96..8110daf03 100644
--- a/tests/sparse_test.py
+++ b/tests/sparse_test.py
@@ -1059,6 +1059,16 @@ class BCOOTest(jtu.JaxTestCase):
     M_dedup = M._dedupe()
     self.assertAllClose(M.todense(), M_dedup.todense())
 
+  def test_bcoo_dedupe_padding(self):
+    # Regression test for https://github.com/google/jax/issues/8163
+    data = jnp.array([1, 0, 0])
+    indices = jnp.array([1, 0, 0])[:, None]
+    x = sparse.BCOO((data, indices), shape=(3,))
+    y = x._dedupe()
+    self.assertArraysEqual(x.todense(), y.todense())
+    self.assertArraysEqual(x.indices, y.indices)
+    self.assertArraysEqual(x.data, y.data)
+
   @parameterized.named_parameters(jtu.cases_from_list(
       {"testcase_name": "_{}_nbatch={}_ndense={}_axes={}".format(
         jtu.format_shape_dtype_string(shape, dtype), n_batch, n_dense, axes),
['tests/sparse_test.py', 'jax/experimental/sparse/bcoo.py']