This paper studies fixed-length compression with multiple constraints in the finite blocklength regime. We introduce two different average distortion measures and consider constraints for individual source outcomes. The concept of d-tilted information as well as recent finite-length bounds for the optimal coding rates are extended to this setting. We further particularise our results to the binary memoryless source and a sparse Gaussian source.

This paper presents a Shannon-type lower bound on the rate-distortion (RD) function of the Bernoulli-Gaussian spike source. The lower bound is valid in all distortion regimes and asymptotically tight for small distortions.

Optimal signaling is studied over a power-limited Gaussian channel with intermittent feedback, where a random mechanism-whose outcome is unknown to the receiver-determines whether or not the output symbol is fed back to the encoder. If the output symbols are fed back with probability smaller than one half, then even the two-messages error probability cannot decay faster than exponentially in the blocklength. But if this probability is greater than one half, then, even for some positive rates, a doubly exponential decay is achievable.

Optimal error probabilities for transmission over the average-power-limited Gaussian channel with intermittent feedback are studied. For the two-message case, the asymptotic decay of the probability of error in the blocklength is double-exponential and is fully characterized. For positive rates a critical rate is identified below which a double-exponential decay is possible and above which it is not.