framing

transmission errors

• problem: transmitting symbols has some errors
• bad cable, radio interference, mismatched clocks, …

  ---

• will get frames with incorrect data
• will get frames with missing/extra data from misdetecting start/end markers
• could pass “bogus” frames to next layer, but…
• better to detect this quickly

checksum idea

• instead of sending ‘‘message’’ .5cm
• say Hash(‘‘message’’) = 0xABCDEF12
• then send ‘‘0xABCDEF12,message’’ .5cm
• when receiving, recompute hash
• discard message if checksum doesn’t match

checksum functions

• hashes used to check messages called checksums

• used at data link layer and upper layers

  • lots of places networks want to check messages aren’t corrupted .5cm

• provides high probability we discard corrupted messages

  • larger checksum \(\rightarrow\) higher probability

example common checksums

• IPv4, TCP —

  • based on one’s complement sum of data+metadata treated as 16-bit numbers
  • one’s complement addition = add normally with wraparound + add carry bit at end
  • efficient to implement on processor with addition
  • easy to compute incrementally

• Ethernet

  • 32-bit ‘‘cyclic redundancy code’’
  • easy to compute fast in hardware
  • always detects up to 3 bits flipped (for sizes used in Ethernet)

size ‘header’

• let’s transmit these (binary) messages:

  • 001
  • 0110
  • 0010

• put 3-bit message size at beginning of messages

• read header, then determine number of bits to read before next header

• assumption: no gaps between messages?

  • need to transmit something in between messages

start/end symbol

• alternate idea: use bit sequence to mark beginning/end
• example choice: send 010 between each frame
• send extra 010s when no frames to send

• problem: messages can contain 010 or end with 01

• one solution: replace 01 in messages with 011

  • (need to undo replacement when receiving)

exercise: overhead

• let’s say start/end symbol is 011
• and we replace 01 with 010 .5cm
• exercise (1): minimum number of bits used to send 1000 bit message?
• exercise (2): maximum number of bits used to send 1000 bit message?

escaping?

• can think of replacement similar to escaping strings in C
  • start/end marker is "
  • " \(\rightarrow\) \"
  • \ \(\rightarrow\) \\
• represent foo \R"3"13\ using "foo \\R\"3\"13\\"
• but needed tweaks to idea to work with bits instead of bytes .5cm
• some physical layers allow transmitting bytes at a time
• framing protocols for those (example: PPP) use -like idea

help from physical layer?

• suppose instead of transmitting 0 or 1

• physical layer transmits 0 or 1 or 2 or 3 or 4

• probably going to ‘waste’ one of these values

  • example: transmit every two bits as 0 or 1 or 2 or 3 .5cm

• idea: take advantage of leftover ‘symbol’ 4

• use it to send start/end

  • similar idea used in many versions of Ethernet

bad choice of start/end (1)

• let’s say we choose delimiter 0000
• what do we need to escape?

  A. any 0000

  A. any 000

  B. any 00

  C. any 0

bad choice of start/end (1)

• sending 10 and 01

  • 100000010000

• sending 1 and 001

  • 100000010000 .5cm

• oops!

• textbook example: start/end = 01111110

  • (and escaping 11111 \(\rightarrow\) 111110)

desynchronization and framing (2)

• with start/end marker idea

  • can have start/end-marker corrupted or added by corruption
  • may mess up multiple frames, but will eventually be resync’d

transmission errors

• problem: transmitting symbols has some errors
• bad cable, radio interference, mismatched clocks, …

  ---

• will get frames with incorrect data
• will get frames with missing/extra data from misdetecting start/end markers
• could pass “bogus” frames to next layer, but…
• better to detect this quickly

checksum idea

• instead of sending ‘‘message’’ .5cm
• say Hash(‘‘message’’) = 0xABCDEF12
• then send ‘‘0xABCDEF12,message’’ .5cm
• when receiving, recompute hash
• discard message if checksum doesn’t match

checksum functions

• hashes used to check messages called checksums

• used at data link layer and upper layers

  • lots of places networks want to check messages aren’t corrupted .5cm

• provides high probability we discard corrupted messages

  • larger checksum \(\rightarrow\) higher probability

example common checksums

• IPv4, TCP —

  • based on one’s complement sum of data+metadata treated as 16-bit numbers
  • one’s complement addition = add normally with wraparound + add carry bit at end
  • efficient to implement on processor with addition
  • easy to compute incrementally

• Ethernet

  • 32-bit ‘‘cyclic redundancy code’’
  • easy to compute fast in hardware
  • always detects up to 3 bits flipped (for sizes used in Ethernet)

framing homework

• implement send+receive messages (strings of bytes) using bits

• send_message(MESSAGE)

• handle_bit_from_network(BIT)

  • calls got_message_function(MESSAGE) .5cm

• but:

  • need to indicate message boundaries somehow
  • need to handle bit flips and missing bits without losing everything

bit bytearrays

# In the given code for the assignment:
def bytes_to_bits(the_bytes):
    result = bytearray()
    for a_byte in the_bytes:
        for i in range(8):
            result.append(0 if (a_byte & (0x1 << i)) == 0 else 1)
    return result

• bytes_to_bytes(b'\x93') ==
bytearray([1,0,0,1, 0,0,1,1])
• using bytearray of 0s and 1s
• (because Python doesn’t have convenient bitarray type)