[Paper Review] Order Optimal Coded Delivery and Caching: Multiple Groupcast Index Coding.

Mingyue Ji, Antonia M. Tulino+2 more|arXiv (Cornell University)|Feb 19, 2014

Caching and Content Delivery12 references16 citations

TL;DR

This paper proposes a novel coded delivery scheme for caching networks with multiple requests per user (L ≥ 1), leveraging multiple groupcast index coding to achieve a multicast codeword length significantly smaller than the naive L-fold application of single-request schemes. The scheme is shown to be approximately optimal, within a constant factor of at most 18, via an information-theoretic converse.

ABSTRACT

The capacity of caching networks has received considerable attention in the past few years. A particularly studied setting is the case of a single server (e.g., a base station) and multiple users, each of which caches segments of files in a finite library. Each user requests one (whole) file in the library and the server sends a common coded multicast message to satisfy all users at once. The problem consists of finding the smallest possible codeword length to satisfy such requests. In this paper we consider the generalization to the case where each user places L ≥ 1 requests. The obvious naive scheme consists of applying L times the order-optimal scheme for a single request, obtaining a linear in L scaling of the multicast codeword length. We propose a new achievable scheme based on multiple groupcast index coding that achieves a significant gain over the naive scheme. Furthermore, through an information theoretic converse we find that the proposed scheme is approximately optimal within a constant factor of (at most) 18.

Motivation & Objective

• Address the inefficiency of naively applying single-request coded caching schemes L times for L requests per user.
• Develop a new achievable scheme that exploits joint coding across multiple user requests to reduce multicast codeword length.
• Establish theoretical limits on the performance of such multi-request caching schemes through an information-theoretic converse.
• Demonstrate that the proposed scheme is approximately optimal, within a constant factor of at most 18, of the theoretical minimum.

Proposed method

• Formulate the multi-request caching problem as a multiple groupcast index coding problem to exploit shared requests and coding gains.
• Design a coded delivery scheme that jointly satisfies all L requests per user using coded multicasting across groups of users with overlapping demands.
• Apply combinatorial groupcasting techniques to minimize the total number of coded transmissions required.
• Use an information-theoretic converse to derive a lower bound on the minimum codeword length, proving the scheme's near-optimality.
• Analyze the scaling behavior of the codeword length with respect to L, showing sub-linear improvement over the naive L-fold scheme.
• Establish a constant-factor approximation guarantee by comparing the proposed scheme's performance to the information-theoretic lower bound.

Experimental results

Research questions

• RQ1 Can a coded caching scheme for multiple requests per user achieve a codeword length significantly smaller than L times the single-request optimal length?
• RQ2 What is the fundamental limit (capacity) of caching networks with L ≥ 1 requests per user?
• RQ3 Can a groupcast-based coding approach exploit request overlaps more efficiently than independent single-request schemes?
• RQ4 How close is the proposed scheme to the information-theoretic lower bound in terms of multiplicative gap?
• RQ5 What is the worst-case constant factor between the proposed scheme and the optimal codeword length?

Key findings

• The proposed scheme achieves a multicast codeword length that is significantly smaller than the naive L-fold application of single-request schemes.
• The scheme is approximately optimal, with a multiplicative gap to the information-theoretic lower bound of at most 18.
• The gain over the naive scheme is substantial, especially as L increases, due to joint coding across multiple requests.
• The information-theoretic converse establishes a lower bound that confirms the near-optimality of the proposed scheme.
• The scheme leverages multiple groupcast index coding to exploit overlaps in user requests, reducing redundant transmissions.
• The constant-factor approximation guarantee holds regardless of the number of users or file library size, under the given model.