bedcmm

Open Implementation of Patented Algorithm (Japan Patent)

This repository provides an open implementation of the "Base Extraction Division Minimum Method," which is registered as a patent in Japan.

• This implementation is intended for research, verification, and evaluation purposes.
• Commercial use or redistribution requires obtaining a license (see below).

bedcmm is a library for robust periodicity, pattern extraction, and communication multiplexing based on a patented method.

Features

A robust algorithm for pattern extraction and periodicity analysis, designed to remain stable under outliers and impulsive noise.

• Quantitative pattern extraction

• Quantitative periodicity calculation

  • Applied to pitch detection robust to impulsive (spike) noise
    https://github.com/YASUHARA-Wataru/bedcmmPitch
  • Periodicity analysis robust to outliers
    (example_temperature_period_ana.py)
  • Support for missing values (NaN)
    • Periodicity can be computed directly without interpolation or preprocessing
    • Outputs the valid data ratio (valid_ratio) as a measure of reliability
    • Shows behavior similar to autocorrelation on complete data, while remaining applicable to datasets with missing values

• Quantitative continuity calculation

• Multiplexing communication using shorter sequences than M-sequences and only 1-bit quantization.However, synchronization is required(only send), randomness is not guaranteed, and signal-to-noise ratio (SNR) is not improved.

• Cross-periodicity analysis (not part of the core patented claims)

  • A method for comparing periodic structures between signals, analogous to the relationship between autocorrelation and cross-correlation

  Note: When the same signal is provided as both inputs, the result corresponds to auto-periodicity.

Install

pip install bedcmm

Example

• pattern

import numpy as np
import bedcmm

np.random.seed(0)

# 周期 + ノイズ
base = np.tile([1, 0, 0, 0], 25)
noise = np.random.randint(0, 2, len(base)) * 0.1

x = base + noise

score = bedcmm.pattern.periodicity(x)

print("periodicity score:", score)

• communication

import numpy as np
import bedcmm

base1 = [False, False, False, False, False, True, True, True]
base2 = [False, False, False, True, False, False, True, True]
base3 = [False, True, False, False, False, False, True, True]
tx1 = np.tile(base1, 5)
tx2 = np.tile(base2, 5)
tx3 = np.tile(base3, 5)

tx = np.array([tx1,tx2,tx3])

send_signal = bedcmm.communication.multiplexing(tx)
print(send_signal)

demod_signal1 = bedcmm.communication.demodulate(send_signal,base1)
demod_signal2 = bedcmm.communication.demodulate(send_signal,base2)
demod_signal3 = bedcmm.communication.demodulate(send_signal,base3)

print("demod_signal1:", demod_signal1)
print("demod_signal2:", demod_signal2)
print("demod_signal3", demod_signal3)

Demo

By running pattern_demo.ipynb and communication_demo.ipynb, you can obtain simple sample results:

A brief explanation is available in the doc directory.

How to run faster

python setup.py build_ext --inplace Run with Cython (pattern modules)

Calculation speed

The benchmark script is speed_test.py.

Cython

       mode      N  time_msec
0    random   1000     2.6160
1    random   5000    61.1024
2    random  10000   245.1453
3  periodic   1000     1.2297
4  periodic   5000    28.6166
5  periodic  10000   110.1707
6     spike   1000     1.3126
7     spike   5000    27.9070
8     spike  10000   113.7231

Python only

       mode      N   time_msec
0    random   1000    188.5421
1    random   5000   4593.9274
2    random  10000  19079.0753
3  periodic   1000    196.6179
4  periodic   5000   4723.4922
5  periodic  10000  18833.8787
6     spike   1000    206.1020
7     spike   5000   4802.0938
8     spike  10000  19601.9191

Patent Information

This algorithm is based on the following Japanese patent:

• Patent Number: JP Patent No. 7537807
• Title: Pattern Extraction and Communication Multiplexing Method
• Registration Date: August 13, 2024
• Summary: Methods for pattern extraction, periodicity calculation, continuity calculation, and communication multiplexing.

Scope of Patent and Non-Patented Implementations

This repository contains both implementations covered by the patent and independent auxiliary or extended implementations.

• Patent-covered components:

  • Core algorithm for pattern extraction and periodicity analysis based on the Base Extraction Division Minimum Method

• Extended implementations:

  • Handling of missing values (NaN)

• Non-patented implementations:

  • Cross-periodicity analysis (e.g., cross_periodicity and related functions)

The applicability of the patent may depend on the specific use case and implementation details.

Contact

fapow.contact[at]gmail.com