View Single Post September 20th, 2006 #1 nic123 Junior Member   Join Date: Jun 2006 Posts: 14 Discovery Checksum Problem Analysis Hello David our resident guru , has analysed the probability of getting one good discovery response when in fact 2 devices are replying at the same time (below) The problem seems to appear a lot more often than I have won the lotto ! Maybe there should be some kind of implementation guide that could recommend having a small backoff timer of some sort to reduce the probability of having this problem. (like ethernet PHYs) Considering most lighting rigs are composed of at least multiple devices of a same manuafcturer that were probably purchased at the same time, I't very possible for an end user to have sequential device IDs. Nic www.enttec.com 1. Discovery Collision Analysis 1.1 Uncorrupted msg MID1 | 0xAA MID1 | 0x55 MID0 | 0xAA MID0 | 0x55 DID3 | 0xAA DID3 | 0x55 DID2 | 0xAA DID2 | 0x55 DID1 | 0xAA DID1 | 0x55 DID0 | 0xAA DID0 | 0x55 ------------- CSUM1 | 0xAA CSUM1 | 0x55 CSUM0 | 0xAA CSUM0 | 0x55 CSUM = (MID1|0xAA + MID0|0xAA + DID3|0xAA + DID2|0xAA + DID1|0xAA + DID0|0xAA) + (MID1|0x55 + MID0|0x55 + DID3|0x55 + DID2|0x55 + DID1|0x55 + DID0|0x55) = (MID1 + MID0 + DID3 + DID2 + DID1 + DID0) + 6*0xFF = (MID1 + MID0 + DID3 + DID2 + DID1 + DID0) + 0x5FA 1.2 Single Bit Corruption Suppose there are 2 responders A and B with UIDs which differ only in DIDx. Collided msg would differ from original msgs A and B in the DIDx bytes and the checksum bytes, as follows. CSUMB - CSUMA = (DIDBx|0xAA + DIDBx|0x55) - (DIDAx|0xAA + DIDAx|0x55) COLLISION(DIDAx|0xAA, DIDBx|0xAA) = (DIDAx | 0xAA) & (DIDBx | 0xAA) = (DIDAx & DIDBx) | 0xAA COLLISION(DIDAx|0x55, DIDBx|0x55) = (DIDAx | 0x55) & (DIDBx | 0x55) = (DIDAx & DIDBx) | 0x55 COLLISION(CSUMA1|0xAA, CSUMB1|0xAA) = (CSUMA1 | 0xAA) & (CSUMB1 | 0xAA) = (CSUMA1 & CSUMB1) | 0xAA COLLISION(CSUMA1|0x55, CSUMB1|0x55) = (CSUMA1 | 0x55) & (CSUMB1 | 0x55) = (CSUMA1 & CSUMB1) | 0x55 COLLISION(CSUMA0|0xAA, CSUMB0|0xAA) = (CSUMA0 | 0xAA) & (CSUMB0 | 0xAA) = (CSUMA0 & CSUMB0) | 0xAA COLLISION(CSUMA0|0x55, CSUMB0|0x55) = (CSUMA0 | 0x55) & (CSUMB0 | 0x55) = (CSUMA0 & CSUMB0) | 0x55 Taking checksum over collided msg gives CSUM(over EUID part of collided msg) - CSUMA = [(DIDAx & DIDBx) | 0xAA] + [(DIDAx & DIDBx) | 0x55] - - [DIDAx | 0xAA] - [DIDAx | 0x55] = (DIDAx & DIDBx) - DIDAx CSUM1(recovered from CSUM part of collided msg) = (CSUMA1 & CSUMB1) CSUM0(recovered from CSUM part of collided msg) = (CSUMA0 & CSUMB0) => CSUM(recovered from CSUM part of collided msg) = CSUMA & CSUMB = CSUMA & [CSUMA + (DIDBx|0xAA) + (DIDBx|0x55) - (DIDAx|0xAA) - (DIDAx|0x55)] = CSUMA & [CSUMA + DIDBx - DIDAx] For collided msg to have good checksum: CSUMA + (DIDAx & DIDBx) - DIDAx = CSUMA & (CSUMA + DIDBx - DIDAx) For the Special Case where DIDBx is obtained from DIDAx by changing a single bit from 0 to 1: bit k of DIDAx = 0 and DIDBx = DIDAx + (1 << k), where 0 <= k <= 7. DIDAx & DIDBx = DIDAx CSUMA = CSUMA & (CSUMA + (1<