[Paper Review] Coded Caching Schemes with Reduced Subpacketization from Linear Block Codes

Li Tang, Aditya Ramamoorthy|arXiv (Cornell University)|May 31, 2017

Caching and Content Delivery21 references4 citations

TL;DR

This paper proposes coded caching schemes with significantly reduced subpacketization levels by leveraging resolvable designs derived from linear block codes with specific rank properties. By exploiting the consecutive column property in generator matrices, the authors achieve subpacketization levels orders of magnitude lower than the original scheme—e.g., reducing from ~4.8×10¹⁴ to ~1.07×10⁹ for K=64, M/N=0.25—while maintaining a modest rate increase, enabling practical deployment in real-world systems.

ABSTRACT

Coded caching is a technique that generalizes conventional caching and promises significant reductions in traffic over caching networks. However, the basic coded caching scheme requires that each file hosted in the server be partitioned into a large number (i.e., the subpacketization level) of non-overlapping subfiles. From a practical perspective, this is problematic as it means that prior schemes are only applicable when the size of the files is extremely large. In this work, we propose coded caching schemes based on combinatorial structures called resolvable designs. These structures can be obtained in a natural manner from linear block codes whose generator matrices possess certain rank properties. We obtain several schemes with subpacketization levels substantially lower than the basic scheme at the cost of an increased rate. Depending on the system parameters, our approach allows us to operate at various points on the subpacketization level vs. rate tradeoff.

Motivation & Objective

• To address the impractically high subpacketization levels in conventional coded caching, which require files to be split into exponentially large numbers of subfiles.
• To reduce subpacketization while maintaining low transmission rates, enabling feasibility in real-world systems with moderate-sized files and storage constraints.
• To establish a systematic link between linear block codes—particularly those with consecutive column rank properties—and low-subpacketization coded caching schemes.
• To provide a flexible tradeoff between subpacketization level and rate, allowing system designers to tune parameters based on application needs.
• To generalize and subsume prior low-subpacketization schemes, such as those based on placement delivery arrays or specific codes like single parity check codes.

Proposed method

• The authors construct coded caching schemes using resolvable combinatorial designs derived from linear block codes whose generator matrices satisfy a consecutive column full-rank property.
• They identify that generator matrices with consecutive column sets of full rank enable the construction of caching schemes with reduced subpacketization.
• The method involves mapping user demands and file subfiles to codewords and subcode structures, ensuring decodability via the rank properties of the code.
• The approach allows for multiple operating points on the subpacketization-rate tradeoff by varying code parameters such as code rate and length.
• Specific constructions are derived from cyclic codes and other linear codes with desirable rank properties, enabling explicit scheme generation.
• The framework generalizes prior schemes, including those based on placement delivery arrays and hypergraph-based designs, by embedding them as special cases.

Experimental results

Research questions

• RQ1 Can coded caching schemes be constructed with subpacketization levels substantially lower than the original scheme’s exponential scaling with K?
• RQ2 How can linear block codes be leveraged to achieve low subpacketization while maintaining acceptable transmission rates?
• RQ3 What structural properties of generator matrices enable the construction of low-subpacketization coded caching schemes?
• RQ4 Can the proposed method achieve a flexible tradeoff between subpacketization and rate across diverse system parameters?
• RQ5 How do the proposed schemes compare in performance to recent works with sublinear or sub-exponential subpacketization scaling?

Key findings

• For K=64 and M/N=0.25, the proposed scheme reduces subpacketization from ~4.8×10¹⁴ (baseline) to ~1.07×10⁹, a reduction of over five orders of magnitude, with only a small rate increase from ~2.82 to 3.
• The scheme achieves F_s ≈ 1.6×10⁴ with R=6 and F_s=64 with R=12 for the same K and M/N, demonstrating a flexible tradeoff between subpacketization and rate.
• The proposed framework subsumes the low-subpacketization scheme of [14] as a special case when using a single parity check code over ℤ/qℤ, even for non-prime-power q.
• Compared to [21], the proposed scheme achieves better subpacketization for certain parameter regimes (e.g., F_s* ≈ 2^b vs. F_s ≈ 2^{2b} when a=2, β=1, m=2b), though [21] may outperform in others.
• For the case M/N ≈ 1/q, the scheme achieves subpacketization F_s* ≈ q^{m²/(8q²)} with rate R ≈ (2q−1)², showing exponential improvement over baseline.
• The method enables schemes with subpacketization scaling sub-exponentially in K, and in some cases linearly, depending on code choice, though full linear scaling requires asymptotically large K as in [16].