Index of refraction measurements are made by means of an optical device in which a coherent light beam is divided into an object beam and a reference beam, each of which is directed through a separate path in a common light transmitting medium. The object beam is also transmitted en route through a test volume that accommodates a substance to be tested. It is subsequently recombined with the reference beam to form a single output beam. The output beam is received by a photo detector and its intensity is measured. The intensity of the detected output beam is related to any phase shift between the object and reference beams. The phase shift in turn is a measure of the index of refraction of the test substance. Information relating to density, temperature and pressure of the test substance can be derived from measured index of refraction values by using conventional conversion formulas. An operating range control is provided by introducing a volume of pressurized gas into the paths of the object and reference beams. The operating range of the instrument is set by adjusting the pressure of the gas in the absence of a test substance.
@cite_16: There is a fundamental relationship between belief propagation and maximum a posteriori decoding. A decoding algorithm, which is called the Maxwell decoder, is introduced and provides a constructive description of this relationship. Both the algorithm itself and the analysis of the new decoder are reminiscent of the Maxwell construction in thermodynamics. This paper investigates in detail the case of transmission over the binary erasure channel, while the extension to general binary memoryless channels is discussed in a companion paper.
@cite_8: We consider communication over mem- oryless channels using low-density parity-check code ensembles above the iterative (belief propagation) threshold. What is the computational complexity of decoding (i.e., of reconstructing all the typical in- put codewords for a given channel output) in this regime? We define an algorithm accomplishing this task and analyze its typical performance. The behav- ior of the new algorithm can be expressed in purely information-theoretical terms. Its analysis provides an alternative proof of the area theorem for the bi- nary erasure channel. Finally, we explain how the area theorem is generalized to arbitrary memoryless channels. We note that the recently discovered rela- tion between mutual information and minimal square error is an instance of the area theorem in the setting of Gaussian channels.
Further, the definition and analysis of a Maxwell decoder' in @cite_8 @cite_16 , is closely related to the approach in this paper. Let us recall that the Maxwell decoder was a (mostly conceptual) algorithm for implementing maximum likelihood decoding of LDPC codes over the erasure channel. The treatment in @cite_8 @cite_16 applies almost verbatim to a simple constraint satisfaction problem known as XORSAT. The generalization in the present paper is analogous to the one from the erasure to a general binary memoryless symmetric channel.