CRC-16 polynomials optimized for applications using self-synchronous scramblers

Performance of Network Coding Schemes for 5g System

“…The 16 bits CRC is generated for each packet at the source node. If the checksum at the destination node is not the same as that of the source node, the received packet is considered as an erroneous packet [16].…”

Transparent generic framing procedure (GFP): a protocol for efficient transport of block-coded data through SONET/SDH networks

“…The drawback to a self-synchronous scrambler, however, is that each transmission error results in a pair of errors (43 bits apart here) in the descrambled data, which means that the superblock CRC must cope with this error multiplication. It has been shown [5,6] that a CRC will preserve its error detection capability in this situation as long as the scambler polynomial and the CRC generator polynomial have no common factors. Unfortunately, all of the standard CRC-16 polynomials contain x + 1 as a factor, which is also a factor in the x 43 + 1 (or any x n + 1) scrambler polynomial.…”

“…Therefore, a new CRC generator polynomial was required that preserved the triple error detecting capability (which is the maximum achievable over this block size) without having any common factors with the scrambler. In order to perform single error correction, the syndromes for single errors and double errors spaced 43 bits apart must all be unique [6]. The code selected for the superblock is x 16 + x 15 + x 12 + x 10 + x 4 + x 3 + x 2 + x + 1, which has both these desired properties, and hence retains its triple error detection and optional single error correction capabilities in the presence of the scrambler [6][7][8].…”

“…An SDCC tunneling application example with transparent GFP. signal into GFP-T in a manner similar to the 8B/10B coded mappings [6].…”