# Data Recording and Transmission: Modulo Counting - Part 18

The mathematics of finite fields and sequences seems to be a long way from everyday life, but it happens in the background every time we use a computer and without it, an explanation of modern error correction cannot be given.

Fig.1 - In two's complement, the circular number field is redefined to begin half a turn away from zero, so zero is in the middle of the scale and positive or negative values can be encoded.

Fig.2 - A three bit twisted ring counter and the sequence it goes through. Mathematically it is raising the starting value a to higher and higher powers.

Fig.3 - The addition, modulo-2, of a pseudo-random sequence to serial data breaks up long run-lengths and reduces any DC component.

Fig.4 - The randomizer used in DVB.

Fig.5 - Here a twisted ring counter is used to calculate redundancy on four data bits A -D to make a 7,4 code. The three redundant bits are left in the register after the data are clocked in.

# Data Recording and Transmission: Delivering Data - Part 23

The requirements for data transmission have changed out of all recognition since the early days of computing where the goal was simply to make something that worked. Today that’s the easy part.

# Data Recording and Transmission: Reed Solomon Codes - Part 22

The Reed Solomon codes are defined by what the decoder expects to see and the encoder has to be configured to suit that.

# Data Recording and Transmission: Reed-Solomon Error Correcting Codes - Part 21

The explosion in digital technology that led to Compact Discs, DVD, personal computers, digital cameras, the Internet and digital television broadcasting relies heavily on a small number of enabling technologies, one of which is the use of Reed-Solomon error correcting…

# Data Recording and Transmission: Burst Errors - Part 20

The first burst error correcting code was the Fire Code, which was once widely used on hard disk drives. Here we look at how it works and how it was used.

# Data Recording and Transmission: Cyclic Redundancy Checks - Part 19

The CRC (cyclic redundancy check) was primarily an error detector, but it did allow some early error correction systems to be implemented. There are many different CRCs but they all work in much the same way, which is that the…