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arXiv:cs/0612053

Deriving Schrodinger Equation From A Soft-Decision Iterative Decoding Algorithm

Xiaofei Huang, Xiaowu Huang

Published Dec 8, 2006• 1 citation
arXivHTMLPDF

Abstract

The belief propagation algorithm has been recognized in the information theory community as a soft-decision iterative decoding algorithm. It is the most powerful algorithm found so far for attacking hard optimization problems in channel decoding. Quantum mechanics is the foundation of modern physics with the time-independent Schrodinger equation being one of the most important equations. This paper shows that the equation can be derived from a generalized belief propagation algorithm. Such a connection on a mathematical basis might shed new insights into the foundations of quantum mechanics and quantum computing.

DOI
10.48550/arxiv.cs/0612053

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The belief propagation algorithm has been recognized in the information theory community as a soft-decision iterative decoding algorithm. It is the most powerful algorithm found so far for attacking hard optimization problems in channel decoding. Quantum mechanics is the foundation of modern physics with the time-independent Schrodinger equation being one of the most important equations. This paper shows that the equation can be derived from a generalized belief propagation algorithm. Such a connection on a mathematical basis might shed new insights into the foundations of quantum mechanics and quantum computing.
One of the greatest scientific achievements of physics in the 20th century is the discovery of quantum mechanics. The Schrodinger equation is the most fundamental equation in quantum mechanics describing the time-based evolution of the quantum state of a physical system. It has been found that the time-independent version of the equation can be derived from a general optimization algorithm. Instead of arguing for a new interpretation and possible deeper principle for quantum mechanics, this paper elaborates a few points of the equation as a general global optimization algorithm. Benchmarked against randomly generated hard optimization problems, this paper shows that the algorithm significantly outperformed a classic local optimization algorithm. The former found a solution in one second with a single trial better than the best one found by the latter around one hour after one hundred thousand trials.
In this paper, an iterative soft-decision (SD) decoding algorithm for cyclic codes based on extended parity-check equations is developed. The algorithm does not necessarily utilize the algebraic properties of the code, but operates on transforming the systematic parity-check matrix using the soft reliability information matrix obtained from the received vector. Results show a significant performance gain when compared with the hard decision Berlekamp-Massey(B-M) and belief propagation (BP) algorithms, but present a similar bit error rate (BER) performance when compared to the adaptive belief propagation (ABP) algorithm. An important feature of the decoder is that it functions within a practical decoding time complexity, and can be generally implemented for the class of linear block codes.
The Schrödinger equation is normally introduced as a foundational postulate of quantum mechanics. In this article, we show that Schrödinger evolution arises naturally from the informational throughput framework defined by three relations connecting energy density to a bounded update capacity χ. Without assuming Hilbert space axioms, wavefunction ontology, or spacetime geometry, conservation of informational throughput forces norm-preserving evolution, which uniquely leads to complex phase rotation and the Schrödinger equation. The result suggests that quantum dynamics may emerge from finite informational processing capacity of physical reality.
In this study, a new method for improving hard-decision bit-flipping (BF) decoding is proposed for low-density parity-check codes. The flipping criterion is derived theoretically from the soft-decision belief-propagation decoding algorithm. The proposed BF decoding algorithm is channel independent and is improved by introducing a more efficient method for computing the reliability of the parity checks. Extensive simulations are provided to demonstrate the efficiency of the proposed algorithm. Simulation results show that the proposed algorithm can achieve about 1.6 dB coding gain improvement at BER=10−5 while reducing up to 53% iterations for decoding and maintaining low-decoding complexity, compared with the conventional weighted BF algorithm.