Lower bounds for adaptive locally decodable codes
Amit Deshpande, Rahul Jain, Telikepalli Kavitha, Satyanarayana V. Lokam, Jaikumar Radhakrishnan · Random Structures and Algorithms · 2005
An error-correcting code is said to be locally decodable if a randomized algorithm can recover any single bit of a message by reading only a small number of symbols of a possibly corrupted encoding of the message. Katz and Trevisan 12 showed that any such code C : {0, 1}n → Σm with a decoding algorithm that makes at most q probes must satisfy m = Ω((n/log |Σ|)q/(q−1)). They assumed that the decoding algorithm is non-adaptive, and left open the question of proving similar bounds for adaptive decoders. We show m = Ω((n/log |Σ|)q/(q−1)) without assuming that the decoder is nonadaptive. © 2005 Wiley Periodicals, Inc. Random Struct. Alg., 2005