kronecker-chenc-for-arduino is an Arduino library that implements the channel encoding algorithm described in the paper by F. Asim et al. for the case of BPSK. The implementation assumes the channel is a binary symmetric channel, that only digital data is sent and received, and that the packets' smallest unit is bytes (8 bits).
Currently, only TPMD-4 with Scheme 2 is implemented, and the decoder implemented is the rank-one detector which has a coding rate of 1/4 due to the need of training symbols.
Drag and drop the files kronecker-chenc.cc and kronecker-chenc.h to the directory where your libraries are installed.
A basic usage example is shown in the next subsection.
#include <Arduino.h>
#include "kronecker-chenc.h"
#define TRAINING_SYMBOLS 0b10101010
void setup() {
// Begin serial monitor
Serial.begin(115200);
/* Do other stuff */
}
void loop() {
uint8_t msg_buffer[1];
// Check for messages
if (Serial.readBytesUntil(0x00, msg_buffer, 1) > 0) {
uint8_t encoded[2] = encode_kronecker_tpmd4s2(msg_buffer[0]);
uint8_t decoded = rank_one_detector_tpmd4s2(encoded[0], encoded[1], TRAINING_SYMBOLS);
Serial.println(decoded, BIN);
}
/* Do other stuff */
}For support or submitting bugs open an issue, I'll check them as soon as I am available.
kronecker-chenc-for-arduino is licensed under the MIT license.
For more information about the algorithm and its performance read the original paper by Fazal E-Asim et al. at https://ieeexplore.ieee.org/document/9146283.
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Since the modulation with Manchester/BPSK is a bijective function, the encoding is applied in the soon-to-be-sent bytes, not on the manchester modulated ones (contrary to what is done on the original paper).
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When using BPSK each symbol is directly linked to 1 bit of information, this makes it possible to use bytes to represent vectors of 8 symbols. The code uses this idea and does every calculation using only bytes (
uint8_t/char/int8_t); however, BPSK symbols have values in {-1, 1} and bits in {0, 1}, so the transformation$F(•)$ is applied where$F(-1) = 0$ $F(1) = 1$ -
$F(a * b) = F(a) \odot F(b) \quad a,b \in \{-1, 1\}$ .
The product is replaced by the negation of the XOR product of the transformed symbols, which has the following truth table and allows to maintain the property that
$-1 * -1 = 1$ .A B XNOR 0 0 1 0 1 0 1 0 0 1 1 1 Table 1: truth table of the XNOR operation