Definition

Randomization in satellite communication is a technique used to improve data transmission reliability and security. Let me explain the key aspects:

Main Purposes of Randomization:

1. Energy Dispersal

• Prevents energy concentration in specific frequencies
• Helps maintain uniform power distribution across the frequency spectrum
• Reduces interference with other satellite systems

2. Encryption & Security

• Makes the transmitted data appear more random
• Helps protect against unauthorized interception
• Part of the overall security framework

3. Error Detection

• Helps in identifying transmission errors
• Makes it easier to detect data corruption
• Improves the effectiveness of error correction

Common Randomization Techniques:

1. Scrambling

• Converts data stream into pseudo-random sequence
• Usually implemented using Linear Feedback Shift Registers (LFSR)
• Often combined with other encoding schemes

2. Data Whitening

• Ensures even distribution of ones and zeros
• Helps maintain timing synchronization
• Reduces DC bias in the transmission

3. Spread Spectrum

• Spreads signal across wider frequency band
• Improves resistance to interference
• Enhances security through signal spreading

Algorithms

There are several algorithms used for randomization in satellite communications.

1. LFSR (Linear Feedback Shift Register) Based:

• Basic LFSR
• Multiple LFSRs in parallel
• Self-synchronizing scrambler
• Multiplicative scrambler
• Additive scrambler

2. PN (Pseudo-Random Number) Sequence Based:

• Gold codes
• Kasami sequences
• Walsh-Hadamard codes
• Maximum length sequences (m-sequences)

3. Block Scramblers:

• Convolutional scramblers
• Multiplicative scramblers with different polynomials
• Frame synchronized scramblers

4. Cryptographic Based:

• AES in counter mode for randomization
• Stream ciphers like ChaCha
• Hash-based generators

Most Common in Practice:
1. CCSDS Standard Randomizer:

• Uses reset scrambler
• Based on LFSR with polynomial: h(x) = x⁸ + x⁷ + x⁵ + x³ + 1
• Widely used in space communications

2. DVB (Digital Video Broadcasting) Randomizer:
   • Uses PRBS (Pseudo Random Binary Sequence)
   • Based on polynomial: 1 + x¹⁴ + x¹⁵

golang package

Built-in Support:
1. Basic PRNG through math/rand and crypto/rand:

import (
    "crypto/rand"
    "math/big"
)

func generateRandomBytes(n int) ([]byte, error) {
    b := make([]byte, n)
    _, err := rand.Read(b)
    return b, err
}

2. For specific randomization algorithms used in satellite communication, you'd typically need to implement them yourself or use third-party packages. Here's an example implementation of an LFSR:

type LFSR struct {
    register uint16
    polynomial uint16
}

func NewLFSR(seed, polynomial uint16) *LFSR {
    return &LFSR{
        register: seed,
        polynomial: polynomial,
    }
}

func (l *LFSR) Next() uint8 {
    // Calculate next bit
    newBit := uint16(0)
    for i := uint16(0); i < 16; i++ {
        if (l.polynomial & (1 << i)) != 0 {
            newBit ^= ((l.register >> i) & 1)
        }
    }
    
    // Shift register and add new bit
    l.register = (l.register << 1) | newBit
    return uint8(l.register & 0xFF)
}

Third-party Packages:
1. github.com/mjibson/go-dsp - For digital signal processing including some randomization
2. Various cryptographic packages that can be used for randomization

Most Common Use Case Implementation (CCSDS Randomizer):

type CCSDSRandomizer struct {
    register uint8
}

func NewCCSDSRandomizer() *CCSDSRandomizer {
    return &CCSDSRandomizer{
        register: 0xFF, // Initial state
    }
}

func (r *CCSDSRandomizer) Randomize(data []byte) {
    for i := range data {
        // CCSDS polynomial: x^8 + x^7 + x^5 + x^3 + 1
        newBit := ((r.register >> 7) ^ (r.register >> 6) ^ 
                   (r.register >> 4) ^ (r.register >> 2)) & 1
        r.register = ((r.register << 1) | newBit) & 0xFF
        data[i] ^= r.register
    }
}

no key for randomization

For randomization in satellite communication, typically no key sharing is needed - the algorithm itself is designed to be self-synchronizing or uses known initialization patterns.

1. Synchronous Scrambling:

• Uses a predefined pattern or polynomial known to both sender and receiver
• Both sides use same LFSR configuration
• Receiver can descramble by applying same algorithm
• Example: CCSDS standard randomizer uses fixed polynomial h(x) = x⁸ + x⁷ + x⁵ + x³ + 1

2. Self-Synchronizing Scrambling:

• Scrambling depends only on previous N bits of transmitted data
• Receiver automatically synchronizes after receiving N bits
• No need for explicit synchronization or key sharing
• Recovers automatically from errors

Example flow:

Sender side:
Original Data -> Scrambler (using standard polynomial) -> Scrambled Data

Receiver side:
Scrambled Data -> Descrambler (using same polynomial) -> Original Data

This is different from encryption because:

• Randomization's goal is signal properties improvement, not security
• Both sides use publicly known, standardized algorithms
• No secret key needed
• Self-synchronizing or uses fixed patterns