CRT Spread Spectrum / CDMA

Multiple users share ONE channel. CRT separates them algebraically. CC0. No patents.

How It Works

Traditional CDMA: each user gets a Walsh-Hadamard spreading code (NxN matrix).
CRT CDMA: the ring Z/970200Z = Z/8 x Z/9 x Z/25 x Z/49 x Z/11 IS the code.

ENCODING (transmit):
  1. Each user i has a unique spreading key k_i in Z/970200Z
  2. User's data symbol d (0-255 byte) is spread: s_i = d * k_i mod N
  3. CRT decomposes s_i into 5 channels: (s mod 8, s mod 9, ..., s mod 11)
  4. All users' channel signals are SUMMED on the shared medium

DECODING (receive):
  1. Receiver knows user i's key k_i
  2. Compute k_i^(-1) mod N (modular inverse exists when gcd(k_i, N) = 1)
  3. Multiply received composite: d_i = S * k_i^(-1) mod N
  4. The CRT structure ensures algebraic separation — no interference

WHY CRT WINS:
  - Walsh-Hadamard: O(N^2) matrix operations, fixed code length
  - CRT: O(1) encode/decode via modular arithmetic, 970200 possible codes
  - 5 independent channels = 5 independent noise dimensions
  - L=11 channel = FREE error detection on every transmission
  - No code assignment authority needed — the algebra IS the protocol

1. Multi-User Transmission

Users:

2. Channel Superposition

All users' signals combined on the shared medium:

Z/8 (D)

Z/9 (K)

Z/25 (E)

Z/49 (b)

Z/11 (L)

3. Receiver Separation

4. Noise Resistance

Noise level: 0%

5. L=11 Error Detection

6. Capacity Comparison

CC0 1.0 Universal - No Rights Reserved. CRT-based spread spectrum using Z/970200Z = Z/8 x Z/9 x Z/25 x Z/49 x Z/11. 5 algebraically orthogonal channels replace Walsh-Hadamard spreading codes. L=11 = free error detection. 970200 unique spreading keys.
No patents. No dependencies. No permission needed. antonlebed.com