Error Exponents of Joint Channel Coding and Intrinsic Randomness for Memoryless Channels

Abstract

This paper considers a joint channel coding and random number generation from channel outputs. Specifically, we want to transmit a message to a receiver reliably and at the same time the receiver extracts pure random bits independent of the channel input. We call this problem as the joint channel coding and intrinsic randomness problem. For stationary memoryless channels, we show exponential upper bounds on both the decoding error probability and the variational distance between the distribution of the obtained random number and the uniform distribution. We also clarify that the obtained both bounds vanish as the block length tends to infinity, whenever a pair of coding rate and random bit rate is within the achievable rate region. Further, the above performance can be obtained by a universal scheme which does not depend on the channel.