diff --git a/composable_kernel/include/tensor_description/dimension.hpp b/composable_kernel/include/tensor_description/dimension.hpp
new file mode 100644
index 0000000000..cd897323a3
--- /dev/null
+++ b/composable_kernel/include/tensor_description/dimension.hpp
@@ -0,0 +1,28 @@
+#ifndef CK_DIMENSION_HPP
+#define CK_DIMENSION_HPP
+
+#include "common_header.hpp"
+
+namespace ck {
+
+template <index_t Length>
+struct Dimension
+{
+    __host__ __device__ static constexpr auto GetLength() { return Number<Length>{}; }
+};
+
+template <index_t Length, index_t Stride>
+struct NativeDimension : Dimension<Length>
+{
+    __host__ __device__ static constexpr auto GetStride() { return Number<Stride>{}; }
+
+    __host__ __device__ static constexpr index_t GetOffset(index_t id) { return id * Stride; }
+
+    __host__ __device__ static constexpr index_t GetOffsetDiff(index_t id_diff)
+    {
+        return id_diff * Stride;
+    }
+};
+
+} // namespace ck
+#endif
diff --git a/composable_kernel/include/tensor_description/dimension_transform.hpp b/composable_kernel/include/tensor_description/dimension_transform.hpp
new file mode 100644
index 0000000000..f8b513ef19
--- /dev/null
+++ b/composable_kernel/include/tensor_description/dimension_transform.hpp
@@ -0,0 +1,217 @@
+#ifndef CK_DIMENSION_TRANSFORM_HPP
+#define CK_DIMENSION_TRANSFORM_HPP
+
+#include "common_header.hpp"
+
+namespace ck {
+
+template <index_t N>
+using MultiIndex = Array<index_t, N>;
+
+// LowLengths: Sequence<...>
+template <class LowLengths>
+struct PassThrough
+{
+    static constexpr index_t nDim = LowLengths::GetSize();
+
+    using LowerId = MultiIndex<nDim>;
+    using UpperId = LowerId;
+
+    __host__ __device__ static constexpr auto GetLowerNumOfDimension() { return Number<nDim>{}; }
+
+    __host__ __device__ static constexpr auto GetUpperNumOfDimension()
+    {
+        return GetLowerNumOfDimension();
+    }
+
+    __host__ __device__ static constexpr auto GetLowerLengths() { return LowLengths{}; }
+
+    __host__ __device__ static constexpr auto GetUpperLengths() { return GetLowerLengths(); }
+
+    __host__ __device__ static constexpr auto GetLowerId(UpperId id_up) { return id_up; }
+
+    __host__ __device__ static constexpr auto GetLowerIdDiff(UpperId id_up_diff)
+    {
+        return id_up_diff;
+    }
+
+    __host__ __device__ static constexpr bool IsLinearTransform() { return true; }
+};
+
+// LowLengths: Sequence<...>
+template <class LowLengths, class LeftPads, class RightPads>
+struct Pad
+{
+    static constexpr index_t nDim = LowLengths::GetSize();
+
+    using LowerId = MultiIndex<nDim>;
+    using UpperId = LowerId;
+
+    __host__ __device__ static constexpr auto GetLowerNumOfDimension() { return Number<nDim>{}; }
+
+    __host__ __device__ static constexpr auto GetUpperNumOfDimension()
+    {
+        return GetLowerNumOfDimension();
+    }
+
+    __host__ __device__ static constexpr auto GetLowerLengths() { return LowLengths{}; }
+
+    __host__ __device__ static constexpr auto GetUpperLengths()
+    {
+        return GetLowerLengths() + LeftPads + RightPads;
+    }
+
+    __host__ __device__ static constexpr auto GetLowerId(UpperId id_up) { return id_up - LeftPads; }
+
+    __host__ __device__ static constexpr auto GetLowerIdDiff(UpperId id_up_diff)
+    {
+        return id_up_diff;
+    }
+
+    __host__ __device__ static constexpr bool IsLinearTransform() { return true; }
+};
+
+// LowLengths: Sequence<...>
+template <class LowLengths>
+struct Merge
+{
+    static constexpr index_t nDimLow = LowLengths::GetSize();
+    static constexpr index_t nDimUp  = 1;
+
+    using LowerId = MultiIndex<nDimLow>;
+    using UpperId = MultiIndex<nDimUp>;
+
+    __host__ __device__ static constexpr auto GetUpperNumOfDimension(){return Number<nDimUp>{}};
+
+    __host__ __device__ static constexpr auto GetLowerNumOfDimension() { return Number<nDimLow>{}; }
+
+    __host__ __device__ static constexpr auto GetLowerLengths() { return LowLengths{}; }
+
+    __host__ __device__ static constexpr auto GetUpperLengths()
+    {
+        return Sequence<accumulate_on_sequence(
+            GetLowerLengths(), math::multiplies<index_t>{}, Number<1>{})>{};
+    }
+
+    __host__ __device__ static constexpr auto GetLowerId(UpperId id_up)
+    {
+        LowerId id_low;
+
+        // not implemeneted
+
+        return id_low;
+    }
+
+    // id_low_diff depends on id_low_old, so id_low need to be up-to-date
+    __host__ __device__ static constexpr auto GetLowerIdDiff(UpperId id_up_diff, LowerId id_low_old)
+    {
+        LowerId id_low_diff;
+
+        // not implemeneted
+
+        return id_low_diff;
+    }
+
+    __host__ __device__ static constexpr bool IsLinearTransform() { return false; }
+};
+
+// UpLengths: Sequence<...>
+template <index_t LowLength, class UpLengths>
+struct Unmerge
+{
+    static constexpr index_t nDimLow = 1;
+    static constexpr index_t nDimUp  = UpLengths::GetSize();
+
+    __host__ __device__ constexpr Unmerge()
+    {
+        static_assert(LowLength == accumulate_on_sequence(
+                                       UpLengths{}, math::multiplies<index_t>{}, Number<1>{}),
+                      "wrong! UpLengths need to be ");
+    }
+
+    __host__ __device__ static constexpr auto GetUpperNumOfDimension(){return Number<nDimUp>{}};
+
+    __host__ __device__ static constexpr auto GetLowerNumOfDimension() { return Number<nDimLow>{}; }
+
+    __host__ __device__ static constexpr auto GetLowerLengths() { return Sequence<LowLength>{}; }
+
+    __host__ __device__ static constexpr auto GetUpperLengths() { return UpLengths{}; }
+
+    __host__ __device__ static constexpr auto GetLowerId(UpperId id_up)
+    {
+        constexpr auto scans = typename sequence_reverse_inclusive_scan<UpLengths,
+                                                                        math::multiplies<index_t>,
+                                                                        1>::type{};
+
+        LowerId id_low{0};
+
+        static_for<0, nDim, 1>{}([&](auto idim) { id_low[0] += id_up[idim] * scans[idim]; });
+
+        return id_low;
+    }
+
+    __host__ __device__ static constexpr auto GetLowerIdDiff(UpperId id_up_diff)
+    {
+        return GetLowerId(id_up_diff);
+    }
+
+    __host__ __device__ static constexpr bool IsLinearTransform() { return true; }
+};
+
+// UpLengths: Sequence<...>
+// Coefficients: Sequence<...>
+// id_low = coefficients[0, ...nDimUp-1] * id_up[0, ...nDimUp-1] + coefficients[nDimUp]
+template <index_t LowLength, class UpLengths, class Coefficients>
+struct Embed
+{
+    static constexpr index_t nDimLow = 1;
+    static constexpr index_t nDimUp  = UpLengths::GetSize();
+
+    static constexpr auto mCoefficients = Coefficients{};
+
+    __host__ __device__ constexpr Embed()
+    {
+        static_assert(UpLengths::GetSize() == nDimUp && Coefficients::GetSize() == nDimUp + 1,
+                      "wrong! # of dimensions not consistent");
+
+        constexpr index_t low_id_max =
+            Coefficents.Back() + accumulate_on_sequence(UpLengths{} * Coefficients::PopBack(),
+                                                        math::plus<index_t>{},
+                                                        Number<0>{});
+
+        static_assert(low_id_max < LowLength, "wrong! lower-id will go out of range");
+    }
+
+    __host__ __device__ static constexpr auto GetUpperNumOfDimension(){return Number<nDimUp>{}};
+
+    __host__ __device__ static constexpr auto GetLowerNumOfDimension() { return Number<nDimLow>{}; }
+
+    __host__ __device__ static constexpr auto GetLowerLengths() { return Sequence<LowLength>{}; }
+
+    __host__ __device__ static constexpr auto GetUpperLengths() { return UpLengths{}; }
+
+    __host__ __device__ static constexpr auto GetLowerId(UpperId id_up)
+    {
+        LowerId id_low{mCoefficients[nDimUp]};
+
+        static_for<0, nDimUp, 1>{}(
+            [&](auto idim) { id_low[0] += id_up[idim] * mCoefficients[idim]; });
+
+        return id_low;
+    }
+
+    __host__ __device__ static constexpr auto GetLowerIdDiff(UpperId id_up_diff)
+    {
+        LowerId id_low_diff{0};
+
+        static_for<0, nDimUp, 1>{}(
+            [&](auto idim) { id_low_diff[0] += id_up_diff[idim] * mCoefficients[idim]; });
+
+        return id_low_diff;
+    }
+
+    __host__ __device__ static constexpr bool IsLinearTransform() { return true; }
+};
+
+} // namespace ck
+#endif
diff --git a/composable_kernel/include/tensor_description/tensor_descriptor.hpp b/composable_kernel/include/tensor_description/tensor_descriptor.hpp
new file mode 100644
index 0000000000..62f23b2bbd
--- /dev/null
+++ b/composable_kernel/include/tensor_description/tensor_descriptor.hpp
@@ -0,0 +1,104 @@
+#ifndef CK_TENSOR_DESCRIPTOR_HPP
+#define CK_TENSOR_DESCRIPTOR_HPP
+
+#include "common_header.hpp"
+#include "dimension.hpp"
+
+namespace ck {
+
+template <class Lengths, class Strides>
+struct NativeTensorDescriptor
+{
+    using type                    = NativeTensorDescriptor;
+    static constexpr index_t nDim = Lengths::GetSize();
+
+    using Id = MultiIndex<nDim>;
+
+    __host__ __device__ static constexpr auto GetNumOfDimension() { return Number<nDim>{}; }
+
+    __host__ __device__ static constexpr auto GetLengths() { return Lengths{}; }
+
+    __host__ __device__ static constexpr auto GetStrides() { return Strides{}; }
+
+    __host__ __device__ static constexpr auto GetLength(index_t IDim) { return Lengths{}[IDim]; }
+
+    __host__ __device__ static constexpr auto GetStride(index_t IDim) { return Strides{}[IDim]; }
+
+    __host__ __device__ static constexpr index_t GetOffset(Id id)
+    {
+        // not implemented
+    }
+};
+
+// LowerTensorDescriptor
+// Transforms: std::tuple<DimensionTransforms...>
+// LowerIds: std::tuple<Sequence<...>>
+// UpperIds: std::tuple<Sequence<...>>
+template <class LowTensorDescriptor,
+          class Transforms,
+          class LowDimensionMasks,
+          class UpDimensionMasks>
+struct TransformedTensorDescriptor
+{
+    using type                       = TransformedTensorDescriptor;
+    static constexpr index_t nDimUp  = xxxx;
+    static constexpr index_t nDimLow = xxx;
+
+    static constexpr index_t nTransform = Transforms::GetSize();
+
+    using UpperId = MultiIndex<nDimUp>;
+    using LowerId = MultiIndex<nDimLow>;
+
+    __host__ __device__ static constexpr TransformedTensorDescriptor()
+    {
+        static_assert(nTransform == Transforms::GetSize() &&
+                          nTransform == LowDimensionMasks::GetSize() &&
+                          nTransform == UpDimensionMasks::GetSize(),
+                      "wrong! # of transformations not the same");
+
+        // TODO: sanity check: LowDimensionMasks should include all low-dimensions,
+        //   UpDimensionMasks should include all up-dimensions
+
+        // TODO: sanity check: while a up-dimension could be associated with multille
+        // transformation,
+        //   a low-dimension should be associated with only one transformation
+    }
+
+    __host__ __device__ static constexpr auto GetNumOfDimension()
+    {
+        // not implemented
+    }
+
+    __host__ __device__ static constexpr auto GetLengths()
+    {
+        // not implemented
+    }
+
+    __host__ __device__ static constexpr auto GetLowerTensorDescriptor()
+    {
+        return LowTensorDescriptor{};
+    }
+
+    __host__ __device__ static constexpr index_t GetLowerId(UpperId id_up)
+    {
+        // not implemented
+    }
+
+    __host__ __device__ static constexpr index_t GetOffset(UpperId id_up)
+    {
+        return GetLowerTensorDescriptor().GetOffset(GetLowerId(id_up));
+    }
+
+    __host__ __device__ static constexpr auto AreUpperId2OffsetLinear();
+    {
+        // not implemented
+    }
+
+    __host__ __device__ static constexpr auto GetIndependentDimensionGroups()
+    {
+        // not implemented
+    }
+};
+
+} // namespace ck
+#endif
diff --git a/composable_kernel/include/utility/common_header.hpp b/composable_kernel/include/utility/common_header.hpp
index b70b61a7a0..a1ec782c9a 100644
--- a/composable_kernel/include/utility/common_header.hpp
+++ b/composable_kernel/include/utility/common_header.hpp
@@ -4,6 +4,7 @@
 #include "config.hpp"
 #include "utility.hpp"
 #include "integral_constant.hpp"
+#include "tuple.hpp"
 #include "math.hpp"
 #include "vector_type.hpp"
 #include "Sequence.hpp"
diff --git a/composable_kernel/include/utility/tuple.hpp b/composable_kernel/include/utility/tuple.hpp
new file mode 100644
index 0000000000..1d91f59ba6
--- /dev/null
+++ b/composable_kernel/include/utility/tuple.hpp
@@ -0,0 +1,68 @@
+#ifndef CK_TUPLE_HPP
+#define CK_TUPLE_HPP
+
+#include "integral_constant.hpp"
+
+namespace ck {
+
+template <class... Ts>
+struct tuple : public std::tuple<Ts...>
+{
+    using type = tuple;
+
+    __host__ __device__ static constexpr index_t GetSize() { return std::tuple_size(tuple{}); }
+
+    template <index_t I>
+    __host__ __device__ constexpr auto Get(Number<I>) const
+    {
+        return std::get<I>(*this);
+    }
+
+    template <index_t I>
+    __host__ __device__ constexpr auto operator[](Number<I>) const
+    {
+        return Get(Number<I>{}) :
+    }
+};
+
+// merge tuple
+template <class... Tuples>
+__host__ __device__ constexpr auto merge_tuple(Tuples&&... xs)
+{
+    return std::tuple_cat(xs...);
+};
+
+// generate sequence
+template <index_t IBegin, index_t NRemain, class F>
+struct tuple_gen_impl
+{
+    static constexpr index_t NRemainLeft  = NRemain / 2;
+    static constexpr index_t NRemainRight = NRemain - NRemainLeft;
+    static constexpr index_t IMiddle      = IBegin + NRemainLeft;
+
+    using type =
+        typename tuple_merge<typename tuple_gen_impl<IBegin, NRemainLeft, F>::type,
+                             typename tuple_gen_impl<IMiddle, NRemainRight, F>::type>::type;
+};
+
+template <index_t I, class F>
+struct tuple_gen_impl<I, 1, F>
+{
+    static constexpr auto x = F{}(Number<I>{});
+    using type              = tuple<Is>;
+};
+
+template <index_t I, class F>
+struct sequence_gen_impl<I, 0, F>
+{
+    using type = Sequence<>;
+};
+
+template <index_t NSize, class F>
+struct sequence_gen
+{
+    using type = typename sequence_gen_impl<0, NSize, F>::type;
+};
+
+} // namespace ck
+#endif