Simon Edwin Crouch

Finding cyclic redundancy check polynomials for multilevel systems

This letter describes a technique for finding cyclic redundancy check polynomials for systems for transmission over symmetric channels which encode information in multiple voltage levels, so that the resulting redundancy check gives good error protection and is efficient to implement. The codes which we construct have a Hamming distance of 3 or 4. We discuss a way to reduce burst error in parallel transmissions and some tricks for efficient implementation of the shift register for these polynomials. We illustrate our techniques by discussing a particular example where the number of levels is 9, but they are applicable in general.

The Design of the IEEE 802.12 Coding Scheme

In 1995, the IEEE approved the 802.12 standard for data transmission at 100-Mbit/s using the Demand Priority Network Access protocol. 100 VG-AnyLAN products conforming to this standard offered an upgrade path for Ethernet and token ring networks, without requiring new building wiring. A key factor in the approval of the 802.12 standard was the demonstrated error detection properties of its coding scheme. In particular, the coding scheme allows the detection of error bursts affecting encoded data carried on four parallel conductors, using nothing more than the standard IEEE 32-bit cyclic redundancy check applied to the unencoded data. Although these error detection properties were presented for verification as part of the standards process, for many years commercial considerations prevented public disclosure of how the code was actually found. These considerations no longer apply, and, in this paper, we explain in detail the design principles of the code, combining geometrical insight, linear algebra, combinatorial reasoning, and computer search.