Abstract-Communication of quantized information is frequently followed by a computation. We consider situations of distributed functional scalar quantization: distributed scalar quantization of (possibly correlated) sources followed by centralized computation of a function. Under smoothness conditions on the sources and function, companding scalar quantizer designs are developed to minimize mean-squared error (MSE) of the computed function as the quantizer resolution is allowed to grow. Striking improvements over quantizers designed without consideration of the function are possible and are larger in the entropy-constrained setting than in the fixed-rate setting. As extensions to the basic analysis, we characterize a large class of functions for which regular quantization suffices, consider certain functions for which asymptotic optimality is achieved without arbitrarily fine quantization, and allow limited collaboration between source encoders. In the entropy-constrained setting, a single bit per sample communicated between encoders can have an arbitrarily large effect on functional distortion. In contrast, such communication has very little effect in the fixed-rate setting.Index Terms-Asymptotic quantization theory, distributed source coding, optimal point density function, rate-distortion theory.

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Abstract-We introduce an electrocardiogram (EKG) preamplifier with a power consumption of 2.8 W, 8.1 V rms input-referred noise, and a common-mode rejection ratio of 90 dB. Compared to previously reported work, this amplifier represents a significant reduction in power with little compromise in signal quality. The improvement in performance may be attributed to many optimizations throughout the design including the use of subthreshold transistor operation to improve noise efficiency, gain-setting capacitors versus resistors, half-rail operation wherever possible, optimal power allocations among amplifier blocks, and the sizing of devices to improve matching and reduce noise. We envision that the micropower amplifier can be used as part of a wireless EKG monitoring system powered by rectified radio-frequency energy or other forms of energy harvesting like body vibration and body heat.Index Terms-Common-mode feedback (CMFB), electrocardiograph (ECG), electrocardiogram (EKG), low noise, low power.

Consider a binary additive noise channel with noiseless feedback. When the noise is a stationary and ergodic process Z, the capacity is 1 − H(Z) (H(·) denoting the entropy rate). It is shown analogously that when the noise is a deterministic sequence z ∞ , the capacity under finite-state encoding and decoding is 1 − ρ(z ∞ ), where ρ(·) is Lempel and Ziv's finite-state compressibility. This quantity is termed the porosity σ(·) of an individual noise sequence. A sequence of schemes are presented that universally achieve porosity for any noise sequence. These converse and achievability results may be interpreted both as a channel-coding counterpart to Ziv and Lempel's work in universal source coding, as well as an extension to the work by Lomnitz and Feder and Shayevitz and Feder on communication across modulo-additive channels. Additionally, a slightly more practical architecture is suggested that draws a connection with finite-state predictability, as introduced by Feder, Gutman, and Merhav.