This poster presents **Bit-IF** (Incremental Sparse Fibers with Bit Encoding), a novel sparse tensor format designed to reduce the storage requirements of large tensors and improve the efficiency of tensor operations, particularly of tensor-vector multiplication (TVM). As datasets in many scientific fields increase in dimensionality, size, and sparsity, efficient storage and computation methods become essential. Current state-of-the-art sparse tensor formats achieve memory-efficient representations but often require extensive indexing or pre-computation, limiting flexibility and efficiency. Unlike existing formats, Bit-IF only records index increments encoded by a compact bit array. This mode-independent approach allows for an arbitrary index traversal during the TVM. Bit-IF's design characteristics significantly reduce memory overhead, improve data locality, and eliminate the need for multiple tensor copies or mode-specific preprocessing before performing a TVM. Our analysis and initial comparative studies show that Bit-IF reduces memory consumption and computation time compared to COO-based approaches. Its mode independence and incremental indexing allow for flexible traversal orders, enabling the use of space-filling curves such as Z-curves or Hilbert curves to improve data locality and scalability. We plan to extend the applicability of this method to other tensor operations, such as tensor-matrix and Khatri-Rao products.