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This paper presents a stochastic algorithm for iterative error control decoding. We show that the stochastic decoding algorithm is an approximation of the sum-product algorithm. When the code's factor graph is a tree, as with trellises, the algorithm approaches maximum a-posteriori decoding. We also demonstrate a stochastic approximations to the alternative update rule successive relaxation. Stochastic decoders have very simple digital implementations which have almost no RAM requirements. We present example stochastic decoders for a trellisbased Hamming code, and for a Block Turbo code constructed from Hamming codes.

This paper presents the design and analysis of a wideband inductorless variable-gain amplifier (VGA) for high-speed communication receiver systems. The proposed methodology of using a dual-feedback network for bandwidth extension and dc offset cancellation is analyzed theoretically. The proof of concept is verified by a measured stand-alone VGA chip and it achieves several record performances compared to the existing publications up to date. The chip achieves a 2.2 GHz 3-dB bandwidth with wide tuning range from 10 dB up to 50 dB. Moreover, it consumes only 2.5 mW through a 1 V supply and occupies 0.01 active area in a standard 90 nm CMOS technology.

Learning Objectives: On successful completion of this activity, participants should be able to (1) provide an introduction to machine learning, neural networks, and deep learning; (2) discuss common machine learning algorithms with illustrative examples and figures; and (3) compare machine learning algorithms and provide guidance on selection for a given application. Financial Disclosure: Sandra E. Black received in-kind funding to her institution from GE Healthcare and Avid Pharmaceuticals. The authors of this article have indicated no other relevant relationships that could be perceived as a real or apparent conflict of interest. CME Credit: SNMMI is accredited by the Accreditation Council for Continuing Medical Education (ACCME) to sponsor continuing education for physicians. SNMMI designates each JNM continuing education article for a maximum of 2.0 AMA PRA Category 1 Credits. Physicians should claim only credit commensurate with the extent of their participation in the activity. For CE credit, SAM, and other credit types, participants can access this activity through the SNMMI website (http://www.snmmilearningcenter.org) through April 2022. This article, the first in a 2-part series, provides an introduction to machine learning (ML) in a nuclear medicine context. This part addresses the history of ML and describes common algorithms, with illustrations of when they can be helpful in nuclear medicine. Part 2 focuses on current contributions of ML to our field, addresses future expectations and limitations, and provides a critical appraisal of what ML can and cannot do.

Abstract-LDPC codes are found in many recent communications standards such as 10GBASE-T, We present a review of a new class of "stochastic" iterative decoding architectures. Stochastic decoders represent probabilistic messages by the frequency of ones in a binary stream. This results in a simple mapping of the factor graph of the code into silicon. An FPGA implementation of a LDPC decoder with 8 information bits and 8 coded bits is described. On an Altera Cyclone FPGA, the throughput is 5 Mbps when clocked at 100 MHz and is expected to increase nearly linearly with the code length. Simulations of the decoder on an Altera Stratix FPGA indicate a potential throughput of 8 Mbps.

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