Blind Index Coding

TL;DR

This paper introduces the blind index coding problem where a sender communicates with multiple users with partial, unknown side information, proposing hybrid coding schemes and bounds to optimize transmission rates under uncertainty.

Contribution

It formulates the blind index coding problem, develops a hybrid coding scheme, and establishes a new outer bound to handle sender uncertainty about user side information.

Findings

Hybrid coding scheme balances rate maximization and interference minimization.

Outer bound effectively captures sender's uncertainty about side information.

Combining repetition with hybrid coding improves rates over erasure channels.

Abstract

We introduce the blind index coding (BIC) problem, in which a single sender communicates distinct messages to multiple users over a shared channel. Each user has partial knowledge of each message as side information. However, unlike classic index coding, in BIC, the sender is uncertain of what side information is available to each user. In particular, the sender only knows the amount of bits in each user's side information but not its content. This problem can arise naturally in caching and wireless networks. In order to blindly exploit side information in the BIC problem, we develop a hybrid coding scheme that XORs uncoded bits of a subset of messages with random combinations of bits from other messages. This scheme allows us to strike the right balance between maximizing the transmission rate to each user and minimizing the interference leakage to others. We also develop a general outer bound, which relies on a strong data processing inequality to effectively capture the senders uncertainty about the users' side information. Additionally, we consider the case where communication takes place over a shared wireless medium, modeled by an erasure broadcast channel, and show that surprisingly, combining repetition coding with hybrid coding improves the achievable rate region and outperforms alternative strategies of coping with channel erasure and while blindly exploiting side information.