We demonstrate a method for encoding and DeCoding the [24,12,8] extended binary Golay code using a simple apparatus. We also present several generalizations of this construction which admit similar DeCoding algorithms.
DeCoding most of the infrared signals can be easily
handled by PIC16C5X microcontrollers. This application
note describes how this DeCoding may be done.
The only mandatory hardware for DeCoding IR signals
is an infrared receiver. The use of two types is
described here. Both are modular types used often by
the consumer electronics industry. The first type
responds to infrared signals modulated at about
40 kHz. The second responds to non-modulated infrared
pulses and has a restricted range. The hardware
costs of each approach will be less than two dollars.
The DeCoding algorithm used in RBDS.c is based on error trapping. The program emulates the operation of the encoder and decoder of a binary cyclic codes, using bitwise shifts and xor for modulo g(x) operations.
Encoding and DeCoding of the binary extended (24,12,8) Golay code:
An arithmetic DeCoding algorithm. It is a very close relative of the error-trapping DeCoding algorithms developed by Kasami in the 1960s.
