diff --git a/jxl/src/error.rs b/jxl/src/error.rs
index ad1be49..5a3ea50 100644
--- a/jxl/src/error.rs
+++ b/jxl/src/error.rs
@@ -67,6 +67,10 @@ pub enum Error {
     InvalidContextMap(u32),
     #[error("Invalid context map: number of histogram {0}, number of distinct histograms {1}")]
     InvalidContextMapHole(u32, u32),
+    #[error("Invalid permutation: skipped elements {skip} and encoded elements {end} don't fit in permutation of size {size}")]
+    InvalidPermutationSize { size: u32, skip: u32, end: u32 },
+    #[error("Invalid permutation: Lehmer code {lehmer} out of bounds in permutation of size {size} at index {idx}")]
+    InvalidPermutationLehmerCode { size: u32, idx: u32, lehmer: u32 },
     // FrameHeader format errors
     #[error("Invalid extra channel upsampling: upsampling: {0} dim_shift: {1} ec_upsampling: {2}")]
     InvalidEcUpsampling(u32, u32, u32),
diff --git a/jxl/src/headers/mod.rs b/jxl/src/headers/mod.rs
index 2f3c2d0..aa414ce 100644
--- a/jxl/src/headers/mod.rs
+++ b/jxl/src/headers/mod.rs
@@ -9,6 +9,7 @@ pub mod encodings;
 pub mod extra_channels;
 pub mod frame_header;
 pub mod image_metadata;
+pub mod permutation;
 pub mod size;
 pub mod transform_data;
 
diff --git a/jxl/src/headers/permutation.rs b/jxl/src/headers/permutation.rs
new file mode 100644
index 0000000..00c68c6
--- /dev/null
+++ b/jxl/src/headers/permutation.rs
@@ -0,0 +1,330 @@
+// Copyright (c) the JPEG XL Project Authors. All rights reserved.
+//
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+use crate::bit_reader::BitReader;
+use crate::entropy_coding::decode::Reader;
+use crate::error::{Error, Result};
+use crate::util::{tracing::instrument, value_of_lowest_1_bit, CeilLog2};
+
+pub struct Permutation(Vec<u32>);
+
+impl std::ops::Deref for Permutation {
+    type Target = [u32];
+
+    fn deref(&self) -> &[u32] {
+        &self.0
+    }
+}
+
+impl Permutation {
+    /// Decode a permutation from entropy-coded stream.
+    pub fn decode(
+        size: u32,
+        skip: u32,
+        br: &mut BitReader,
+        entropy_reader: &mut Reader,
+    ) -> Result<Self> {
+        let end = entropy_reader.read(br, get_context(size))?;
+        Self::decode_inner(size, skip, end, |ctx| entropy_reader.read(br, ctx))
+    }
+
+    fn decode_inner(
+        size: u32,
+        skip: u32,
+        end: u32,
+        mut read: impl FnMut(usize) -> Result<u32>,
+    ) -> Result<Self> {
+        if end > size - skip {
+            return Err(Error::InvalidPermutationSize { size, skip, end });
+        }
+
+        let mut lehmer = Vec::new();
+        lehmer.try_reserve(end as usize)?;
+
+        let mut prev_val = 0u32;
+        for idx in skip..(skip + end) {
+            let val = read(get_context(prev_val))?;
+            if val >= size - idx {
+                return Err(Error::InvalidPermutationLehmerCode {
+                    size,
+                    idx,
+                    lehmer: val,
+                });
+            }
+            lehmer.push(val);
+            prev_val = val;
+        }
+
+        // Initialize the full permutation vector with skipped elements intact
+        let mut permutation: Vec<u32> = Vec::new();
+        permutation.try_reserve((size - skip) as usize)?;
+        permutation.extend(0..size);
+
+        // Decode the Lehmer code into the slice starting at `skip`
+        let permuted_slice = decode_lehmer_code(&lehmer, &permutation[skip as usize..])?;
+
+        // Replace the target slice in `permutation`
+        permutation[skip as usize..].copy_from_slice(&permuted_slice);
+
+        // Ensure the permutation has the correct size
+        assert_eq!(permutation.len(), size as usize);
+
+        Ok(Self(permutation))
+    }
+}
+
+// Decodes the Lehmer code in `code` and returns the permuted slice.
+#[instrument(ret, err)]
+fn decode_lehmer_code(code: &[u32], permutation_slice: &[u32]) -> Result<Vec<u32>> {
+    let n = permutation_slice.len();
+    if n == 0 {
+        return Err(Error::InvalidPermutationLehmerCode {
+            size: 0,
+            idx: 0,
+            lehmer: 0,
+        });
+    }
+
+    let mut permuted = vec![];
+    permuted.try_reserve(n)?;
+    permuted.extend_from_slice(permutation_slice);
+
+    let padded_n = (n as u32).next_power_of_two() as usize;
+
+    // Allocate temp array inside the function
+    let mut temp = vec![];
+    temp.try_reserve(padded_n)?;
+    temp.extend((0..padded_n as u32).map(|x| value_of_lowest_1_bit(x + 1)));
+
+    for (i, permuted_item) in permuted.iter_mut().enumerate() {
+        let code_i = *code.get(i).unwrap_or(&0);
+
+        // Adjust the maximum allowed value for code_i
+        if code_i as usize > n - i - 1 {
+            return Err(Error::InvalidPermutationLehmerCode {
+                size: n as u32,
+                idx: i as u32,
+                lehmer: code_i,
+            });
+        }
+
+        let mut rank = code_i + 1;
+
+        // Extract i-th unused element via implicit order-statistics tree.
+        let mut bit = padded_n;
+        let mut next = 0usize;
+        while bit != 0 {
+            let cand = next + bit;
+            if cand == 0 || cand > padded_n {
+                return Err(Error::InvalidPermutationLehmerCode {
+                    size: n as u32,
+                    idx: i as u32,
+                    lehmer: code_i,
+                });
+            }
+            bit >>= 1;
+            if temp[cand - 1] < rank {
+                next = cand;
+                rank -= temp[cand - 1];
+            }
+        }
+
+        *permuted_item = permutation_slice[next];
+
+        next += 1;
+        while next <= padded_n {
+            temp[next - 1] -= 1;
+            next += value_of_lowest_1_bit(next as u32) as usize;
+        }
+    }
+
+    Ok(permuted)
+}
+
+// Decodes the Lehmer code in `code` and returns the permuted vector.
+#[cfg(test)]
+fn decode_lehmer_code_naive(code: &[u32], permutation_slice: &[u32]) -> Result<Vec<u32>> {
+    let n = code.len();
+    if n == 0 {
+        return Err(Error::InvalidPermutationLehmerCode {
+            size: 0,
+            idx: 0,
+            lehmer: 0,
+        });
+    }
+
+    // Ensure permutation_slice has sufficient length
+    if permutation_slice.len() < n {
+        return Err(Error::InvalidPermutationLehmerCode {
+            size: n as u32,
+            idx: 0,
+            lehmer: 0,
+        });
+    }
+
+    // Create temp array with values from permutation_slice
+    let mut temp = permutation_slice.to_vec();
+    let mut permuted = Vec::with_capacity(n);
+
+    // Iterate over the Lehmer code
+    for (i, &idx) in code.iter().enumerate() {
+        if idx as usize >= temp.len() {
+            return Err(Error::InvalidPermutationLehmerCode {
+                size: n as u32,
+                idx: i as u32,
+                lehmer: idx,
+            });
+        }
+
+        // Assign temp[idx] to permuted vector
+        permuted.push(temp.remove(idx as usize));
+    }
+
+    // Append any remaining elements from temp to permuted
+    permuted.extend(temp);
+
+    Ok(permuted)
+}
+
+fn get_context(x: u32) -> usize {
+    (x + 1).ceil_log2().min(7) as usize
+}
+
+#[cfg(test)]
+mod test {
+    use super::*;
+    use arbtest::arbitrary::{self, Arbitrary, Unstructured};
+    use core::assert_eq;
+    use test_log::test;
+
+    #[test]
+    fn generate_permutation_arbtest() {
+        arbtest::arbtest(|u| {
+            let input = PermutationInput::arbitrary(u)?;
+
+            let permutation_slice = input.permutation.as_slice();
+
+            let perm1 = decode_lehmer_code(&input.code, permutation_slice);
+            let perm2 = decode_lehmer_code_naive(&input.code, permutation_slice);
+
+            assert_eq!(
+                perm1.map_err(|x| x.to_string()),
+                perm2.map_err(|x| x.to_string())
+            );
+            Ok(())
+        });
+    }
+
+    #[derive(Debug)]
+    struct PermutationInput {
+        code: Vec<u32>,
+        permutation: Vec<u32>,
+    }
+
+    impl<'a> Arbitrary<'a> for PermutationInput {
+        fn arbitrary(u: &mut Unstructured<'a>) -> Result<Self, arbitrary::Error> {
+            // Generate a reasonable size to prevent tests from taking too long
+            let size_lehmer = u.int_in_range(1..=1000)?;
+
+            let mut lehmer: Vec<u32> = Vec::with_capacity(size_lehmer as usize);
+            for i in 0..size_lehmer {
+                let max_val = size_lehmer - i - 1;
+                let val = if max_val > 0 {
+                    u.int_in_range(0..=max_val)?
+                } else {
+                    0
+                };
+                lehmer.push(val);
+            }
+
+            let mut permutation = Vec::new();
+            let size_permutation = u.int_in_range(size_lehmer..=1000)?;
+            permutation.extend(0..size_permutation);
+
+            let num_of_swaps = u.int_in_range(0..=100)?;
+            for _ in 0..num_of_swaps {
+                // Randomly swap two positions
+                let pos1 = u.int_in_range(0..=size_permutation - 1)?;
+                let pos2 = u.int_in_range(0..=size_permutation - 1)?;
+                permutation.swap(pos1 as usize, pos2 as usize);
+            }
+
+            Ok(PermutationInput {
+                code: lehmer,
+                permutation,
+            })
+        }
+    }
+
+    #[test]
+    fn simple() {
+        // Lehmer code: [1, 1, 2, 3, 3, 6, 0, 1]
+        let code = vec![1u32, 1, 2, 3, 3, 6, 0, 1];
+        let skip = 4;
+        let size = 16;
+
+        let permutation_slice: Vec<u32> = (skip..size).collect();
+
+        let permuted = decode_lehmer_code(&code, &permutation_slice).unwrap();
+        let permuted_naive = decode_lehmer_code_naive(&code, &permutation_slice).unwrap();
+
+        let mut permutation = Vec::with_capacity(size as usize);
+        permutation.extend(0..skip); // Add skipped elements
+        permutation.extend(permuted.iter());
+        let expected_permutation = vec![0, 1, 2, 3, 5, 6, 8, 10, 11, 15, 4, 9, 7, 12, 13, 14];
+
+        assert_eq!(permutation, expected_permutation);
+        assert_eq!(permuted, permuted_naive);
+    }
+
+    #[test]
+    fn decode_lehmer_compare_different_length() -> Result<(), Box<dyn std::error::Error>> {
+        // Lehmer code: [1, 1, 2, 3, 3, 6, 0, 1]
+        let code = vec![1u32, 1, 2, 3, 3, 6, 0, 1];
+        let skip = 4;
+        let size = 16;
+
+        let permutation_slice: Vec<u32> = (skip..size).collect();
+
+        let permuted_optimized = decode_lehmer_code(&code, &permutation_slice)?;
+        let permuted_naive = decode_lehmer_code_naive(&code, &permutation_slice)?;
+
+        let expected_permuted = vec![5u32, 6, 8, 10, 11, 15, 4, 9, 7, 12, 13, 14];
+
+        assert_eq!(permuted_optimized, expected_permuted);
+        assert_eq!(permuted_naive, expected_permuted);
+        assert_eq!(permuted_optimized, permuted_naive);
+
+        Ok(())
+    }
+
+    #[test]
+    fn decode_lehmer_compare_same_length() -> Result<(), Box<dyn std::error::Error>> {
+        // Lehmer code: [2, 3, 0, 0, 0]
+        let code = vec![2u32, 3, 0, 0, 0];
+        let n = code.len();
+        let permutation_slice: Vec<u32> = (0..n as u32).collect();
+
+        let permuted_optimized = decode_lehmer_code(&code, &permutation_slice)?;
+        let permuted_naive = decode_lehmer_code_naive(&code, &permutation_slice)?;
+
+        let expected_permutation = vec![2u32, 4, 0, 1, 3];
+
+        assert_eq!(permuted_optimized, expected_permutation);
+        assert_eq!(permuted_naive, expected_permutation);
+        assert_eq!(permuted_optimized, permuted_naive);
+
+        Ok(())
+    }
+
+    #[test]
+    fn lehmer_out_of_bounds() {
+        let code = vec![4];
+        let permutation_slice: Vec<u32> = (4..8).collect();
+
+        let result = decode_lehmer_code(&code, &permutation_slice);
+        assert!(result.is_err());
+    }
+}
diff --git a/jxl/src/util.rs b/jxl/src/util.rs
index 6e879ff..1245160 100644
--- a/jxl/src/util.rs
+++ b/jxl/src/util.rs
@@ -3,12 +3,14 @@
 // Use of this source code is governed by a BSD-style
 // license that can be found in the LICENSE file.
 
+mod bits;
 #[allow(unused)]
 mod concat_slice;
 mod log2;
 mod shift_right_ceil;
 pub mod tracing;
 
+pub use bits::*;
 #[allow(unused)]
 pub use concat_slice::*;
 pub use log2::*;
diff --git a/jxl/src/util/bits.rs b/jxl/src/util/bits.rs
new file mode 100644
index 0000000..fe578ea
--- /dev/null
+++ b/jxl/src/util/bits.rs
@@ -0,0 +1,23 @@
+// Copyright (c) the JPEG XL Project Authors. All rights reserved.
+//
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+pub fn value_of_lowest_1_bit(t: u32) -> u32 {
+    t & t.wrapping_neg()
+}
+#[cfg(test)]
+mod test {
+    use super::*;
+
+    #[test]
+    fn test_value_of_lowest_1_bit() {
+        assert_eq!(value_of_lowest_1_bit(0b0001), 1);
+        assert_eq!(value_of_lowest_1_bit(0b1111), 1);
+        assert_eq!(value_of_lowest_1_bit(0b0010), 2);
+        assert_eq!(value_of_lowest_1_bit(0b0100), 4);
+        assert_eq!(value_of_lowest_1_bit(0b1010), 2);
+        assert_eq!(value_of_lowest_1_bit(0b1000_0000), 128);
+        assert_eq!(value_of_lowest_1_bit(0), 0);
+    }
+}