Mechanistic Analysis of Signal Amplification and Information Compression: A Comparative Study Based on Traditional Information Theory and Structural Conservation

Author: Zhang Suhang, Luoyang, Henan

Abstract

Signal amplification and lossless information compression are two types of fundamental transformation operations in information transmission and storage systems. Traditional information theory, with statistical entropy as its core metric, can perform numerical calculations of information content for both types of operations, but it cannot provide an essential explanation of the underlying invariance mechanism of the transformations. Based on an idealized research paradigm, this paper strips away secondary interference factors such as noise, distortion, and loss, and analyzes the technical mechanisms and transformation characteristics of linear signal amplification and lossless data compression under an idealized system model. It compares the explanatory limitations of traditional information theory with the explanatory completeness of structural conservation theory. The study shows that both signal amplification and lossless information compression belong to parameter transformations at the carrier dimension, and neither alters the intrinsic structure and logical relations of information. Traditional information theory can only describe the invariance of statistical quantities of information, whereas structural conservation can uniformly characterize the essential laws of both types of information transformations.

Keywords: signal amplification; lossless compression; information structure; structural conservation

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I Introduction

In modern information systems, the transmission, storage, and processing of information are all realized through physical transformations of signal carriers and data encoding transformations. Signal amplification is used to solve the problem of signal power attenuation during transmission and is a fundamental front-end operation in communication systems; information compression is used to eliminate data redundancy and reduce storage and transmission bandwidth overhead, and is a core technology in the field of information storage.

For a long time, the academic community has relied on traditional information theory to conduct quantitative analysis of these two types of transformations, forming the general conclusion that "under ideal transformations, information entropy remains constant." This conclusion is a numerical statistical result, not a mechanistic explanation: traditional theory cannot answer why two types of operations with completely different physical properties and transformation dimensions can both fully preserve the original information.

Referring to the idealized research paradigm, investigating the essential laws of things requires stripping away external interfering factors. This paper removes non-ideal factors such as noise interference, nonlinear distortion, and compression loss, constructs a pure idealized transformation model, and by dismantling the underlying details of the two types of technologies, compares the explanatory power of traditional theory and structural conservation theory, thereby revealing the core invariant of information transformation.

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II The Technical Mechanism and Transformation Characteristics of Signal Amplification Under Ideal Conditions

2.1 Technical Definition of Linear Ideal Amplification

In engineering, ideal signal amplification specifically refers to linear noise-free power amplification, which satisfies strict linear transformation conditions, with the general time-domain transformation formula:

y(t) = A · x(t)

Where x(t) is the original input signal, y(t) is the amplified output signal, and A is a constant amplification factor (constant, A > 1).

This ideal model strictly removes three types of secondary interference: the superposition interference of circuit thermal noise and channel noise; transistor nonlinear distortion and saturation distortion; and additional distortions such as phase shift and frequency attenuation.

2.2 Core Transformation Details of Signal Amplification

Decomposed from the physical dimension, ideal signal amplification involves only quantitative scaling at the dimensions of signal energy and amplitude:

1. Time-domain characteristics: the instantaneous values of the signal at all moments are scaled proportionally; the waveform shape, extremum positions, pulse timing, and period/frequency of the signal remain completely unchanged;

2. Frequency-domain characteristics: performing a Fourier transform on the signal yields Y(ω) = A · X(ω); the spectral structure, frequency components, and phase relations of the signal are unchanged, with only the spectral amplitude raised overall;

3. Information carrier changes: the signal voltage, power, and propagation coverage capability are enhanced, belonging to quantitative changes in the physical parameters of the carrier.

2.3 Traditional Information Theory's Explanation of Signal Amplification

According to the traditional information entropy formula:

H(X) = − Σ p(x_i) log₂ p(x_i)

In the ideal amplification process, the probability distribution p(x_i) of random events carried by the signal remains unchanged, so the information entropy H(X) is strictly constant.

This explanation has limitations: traditional theory only proves through statistical probability that "the amount of information is not lost," without paying attention to the waveform structure, frequency topology, or temporal correlations of the signal. It cannot explain: after core physical parameters such as amplitude and power have completely changed, why information possesses complete restorability and consistency.

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III The Technical Mechanism and Transformation Characteristics of Lossless Information Compression Under Ideal Conditions

3.1 Technical Definition of Lossless Compression

Lossless compression is an encoding transformation based on the elimination of source redundancy. Under ideal error-free decoding conditions, the original data can be uniquely and precisely restored from the compressed data, with no information loss throughout. Common algorithms include Huffman coding, LZW coding, arithmetic coding, etc.

The research model of this paper removes interfering factors such as decoding errors, bit errors, and encoding truncation, satisfying strict encoding reversibility conditions.

3.2 Core Transformation Details of Lossless Compression

Lossless compression does not change the physical form of the signal; it only completes structural optimization of the data encoding carrier. Its core technical characteristics are as follows:

1. Redundancy elimination logic: targeting symbol repetition, uneven probability, and fixed-format redundancy present in the source, by reallocating code lengths—assigning short codes to high-probability symbols and long codes to low-probability symbols—the overall data bit length is reduced;
2. Invariance of logical structure: the symbol associations, sequence order, logical mappings, and semantic topology of the original data are completely preserved; the encoding transformation is merely an equivalent substitution of the form of data expression;
3. Transformation reversibility: compression encoding and decompression decoding constitute a bijective transformation, with input and output data in one-to-one correspondence, with no ambiguity, no loss, and no reconstruction deviation.

3.3 Traditional Information Theory's Explanation of Lossless Compression

The traditional source coding theorem states: the limit of lossless compression is the source information entropy; after ideal compression, the average code length of the data infinitely approaches the entropy value, and the overall information entropy of the system remains constant.

Consistent with signal amplification, traditional theory can only achieve a numerical conservation determination of information content. It only quantifies the increase or decrease of bit redundancy, without paying attention to the internal logical structure, relational relations, or ontological form of information within the data, and cannot essentially explain the principle of information preservation in compression transformations.

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IV The Unified Limitations of Traditional Information Theory

Signal amplification is an energy-amplitude transformation in the physical domain, while lossless compression is an encoding-structure transformation in the digital domain. The transformation dimensions, physical mechanisms, and engineering uses of the two types of technology are completely different.

Under the traditional framework, the two share only the statistical conclusion of "entropy invariance," and there is no unified underlying logic. The core limitations of traditional information theory can be summarized in two points:

1. Emphasis on statistics over structure: taking probability statistics, bit quantity, and entropy value as the sole metrics, detached from the structural essence of information;
2. Fragmented explanation: unable to incorporate two heterogeneous information transformations into a single theoretical system for explanation, only able to verify numerical results individually, and unable to reveal the common essence of the transformations.

In short, traditional information theory can only answer "the amount of information after transformation has not changed," but cannot answer "why the essence of information after transformation has not changed."

In the traditional framework, amplification and compression share only one common point: "entropy invariance." This common point is numerical, not mechanistic. A numerical common point does not constitute unification.

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V Structural Conservation's Unified Mechanistic Explanation of the Two Types of Information Transformation

Structural conservation theory takes the intrinsic structure of information as its core object of study and can uniformly explain the essential laws of signal amplification and lossless compression under ideal conditions.

5.1 Core Definitions

Information structure refers to the sum of the temporal relations, topological forms, logical associations, and element proportions carried by an information carrier. It is the core of the information ontology, distinct from carrier energy and encoding form.

Structural conservation means: in ideal interference-free information-equivalent transformations, the external carrier parameters of information may change arbitrarily, while the intrinsic core structure remains constant.

This paper takes restorability as the criterion of structure: what can be precisely restored means the structure has been preserved; what cannot be restored means the structure has been damaged.

5.2 The Structural Conservation Mechanism of Signal Amplification

In ideal linear amplification, the time-domain waveform structure, frequency-domain frequency structure, phase topological structure, and temporal correlation structure of the signal are all constant.

The amplification operation only changes external physical attributes of the carrier such as power and amplitude, without causing any disturbance to the proportions, positions, or relational relations of the internal elements of the signal. Therefore, the signal can be completely restored to its original form through an inverse attenuation transformation. The essence is the complete restorability of information brought about by structural constancy.

5.3 The Structural Conservation Mechanism of Lossless Compression

The encoding reconstruction process of lossless compression only optimizes the length and format of the external encoding carrier of the data. The symbol sequence structure, logical mapping structure, and semantic association structure of the original data are completely conserved.

Redundancy is invalid additional data of the carrier, not the information ontology. Eliminating redundancy does not destroy the core structure, so the original information can be precisely replicated after decoding.

5.4 Theoretical Comparison

1. Traditional information theory: statistical numerical conservation, quantitative description at the phenomenal level, fragmented, no unified mechanism;
2. Structural conservation theory: ontological structural conservation, mechanistic explanation at the essential level, capable of unifying all equivalent information transformations.

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VI Conclusion

By dismantling the engineering technical details of linear signal amplification and lossless data compression, and combining this with the idealized research paradigm, this paper compares the explanatory power of traditional information theory and structural conservation theory.

The study confirms: traditional information theory can only achieve numerical statistical verification of information transformations, and has inherent limitations of emphasizing statistics over essence and fragmented explanation, unable to mechanistically explain the information preservation logic of fundamental information transformations. Structural conservation theory, taking the intrinsic structure of information as the core invariant, uniformly explains the underlying mechanisms of signal amplification in the physical domain and information compression in the digital domain, and distinguishes the boundary between information carrier and information ontology.

Non-ideal factors such as noise, distortion, and lossy compression are external additional disturbances, which are damage to and deviation of information structure, and do not negate the essence of structural conservation under ideal conditions. Structural conservation provides a new theoretical framework for research on the underlying mechanisms of information transformation, information transmission, and information encoding.

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References

Omitted