Outline: Error Checking

• ATM Conclusion
• Parity
• Checksum
• CRC
• LAN latency

ATM Switch Buffering

• Without buffers, can only handle exact permutations
• Input Buffering:
  • Buffer is between input port and crossbar
  • Head-of-line blocking: packets for a free port blocked by packets at the "head of the line" for a congested port
• Output Buffering:
  • No head-of-line blocking
  • Buffer must be able to accept N cells for each cell sent
• Priority Buffers (low priority cells can't block high priority cells)

ATM Questions

• What does QoS give us that a few priorities wouldn't?
• Is connection-oriented the right model?
• How expensive is non-reordering of cells, and is it worth it?
• Why is ATM more expensive than Ethernet?
• ATM Scalability: (155Mb/s, 622Mb/s, 2.4Gb/s, 10Gb/s....) how far can it go?

Error Checking

• Detect bit errors and burst errors.
• Think of an error pattern as being XOR'd with the original message.
• example:

  message =	01010101 11110000
  error =	00010000 01000000
  received data =	01000101 10110000

Parity

• Add a bit to every byte:
  • even parity, add the XOR of the bits
  • odd parity add the XNOR.
• ASCII has seven bits, so adding a bit makes it into an even byte.
• Performance: Detects
  • all single-bit errors
  • about (n - 1)/n two-bit errors (in messages of n bytes)
  • Also detects about x/2 burst errors of length x bytes.
  • Overhead is (1 / 7) =~ 14%.

Checksum

• 16-bit Internet checksum used for:
  • IP header
  • TCP (mandatory): header, pseudo-header, and data
  • UDP (optional)
  • other Internet protocols.
• Described in in RFC 1071

Checksum

• Transmission:
  • The checksum is the negation
  • of the 1's complement sum
  • of all pairs of bytes (padded with a zero byte if needed).
• Checking:
  • same computation, result must be 0xffff.
• Performance: Detects
  • all single-bit errors
  • almost all actual burst errors
  • does not detect reorderings.
  • for messages of n bytes, overhead is (2 / n)
  • =~ 9.5% for n = 21, =~ 0.1% for n = 1500.

1's complement addition

• Like binary (2's complement) arithmetic, but
• when addition has a carry, the carry is added back in to the result

Example 1's complement addition

• Using a 32-bit value to compute the 16-bit checksum
• carries can be accumulated in the more significant half
• then added in at the end.
• The computation is commutative, associative, and byte-order independent. (2's complement addition is not byte-order independent)

CRC

• polynomial remainder
• bit remainder
• shift registers
• used in:
  • Ethernet
  • FDDI
  • ATM
  • many other protocols.

CRC Performance

• Detect all all single-bit errors
• all double-bit errors
• all odd-numbered errors
• any burst of length less than k bits
• and reorderings.
• For messages of n bytes, overhead is (k / 8n) .
• e.g. the overhead is 6.7% for k = 32 and n = 60.

LAN latency

• time from availability of packet at network interface (API?) to delivery at network interface
• sum of:
  • queueing time Q (machine local queue)
  • medium access time M (e.g. collision, FDDI)
  • transmission time N/B (packet size / link rate)
  • propagation time D/S (distance / speed of signal)
• t = Q + M + N/B + D/S