Channel Allocation and Multislot Coding for Multichannel ALOHA with Deadlines

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Channel Allocation and Multislot Coding for
Multichannel ALOHA with Deadlines

• Dror Baron
• Supervisor Dr. Yitzhak Birk
• MSc. Thesis in Electrical Engineering
• June 1999

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Outline

• Introduction
• Previous work
• Main issues in the work
• Multiple working points
• Multislot messages
• Additional issues
• Conclusions

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Classical ALOHA

• Numerous stations
• Contention stationgtsatellite uplink
• Simultaneous transmissions collide
• Time slots
• No carrier sense
• Feedback rounds
• Acks and system control done by contention-free
  HUB downlink

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Multichannel ALOHA

• Single channel
• Immediate retransmissions would cause
  repetitive collisions
• Random backoff on failure
• Increasing mean backoff time for stability
• Multichannel ALOHA
• Channel randomization
• Immediate retransmissions do not always collide

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Classical Performance Measures

• Pc - collision probability
• G - offered load
• S - capacity
• EN - expected number of transmissions
• T - mean delay
• Assuming Poisson arrivals
• Pc1-e-G
• EN eG

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Classical Research Directions

• Increase capacity
• Several power levels
• Collision resolution algorithms
• Delay-throughput trade-offs
• Stability
• Multichannel ALOHA
• Multicopy - several copies per round

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Delay-Constrained Capacity BK98

• User defined deadline in time
• System deadline in slots Ds
• Round-oriented deadline Dr
• Permissible probability of missing deadline Pe
• Design constraint (Pe, Dr)
• Design goal maximize capacity
• Generation rate Sg vs. capacity SSg(1-Pe)

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Nonstationary Multicopy BK98

• Nonstationary number of copies
• More copies in later rounds
• Benefit higher probability of success
• Cost redundant copies
• Optimization method dynamic programming
• Additional issue block erasure coding in a
  single round

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Single Transmitter Round Stretching
Multiple transmitters
Single transmitter
slot

• Multiple copies with a single transmitter stretch
  the round
• Number of permissible rounds could go down

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Main Issues in this Work

• Single slot messages
• Same problem definition as BK98
• New methods (MWP, impure)
• Multislot messages
• Block erasure codes
• Channel reservation by HUB

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Multiple Working Points

• Nonstationary multicopy BK98
• Probability that all copies transmitted in a
  later round collide is decreased by transmitting
  a larger number of copies in later rounds
• Cost excessive copies
• Single copy multiple working point
• Same goal achieved by using lightly loaded
  channels for later rounds
• Cost inefficient utilization of these channels
• The two approaches can be combined

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Comparing Mechanisms

• SWP nonstationary
• Pe decays exponentially with total number of
  copies
• Channel capacity only slightly degraded
• Total max number of copies Nmax is logarithmic in
  Pe
• Rise in EN is much slower
• MWP single copy
• Last round needs to have very clean working point
• Lots of channels necessary for this
• Channel capacity significantly degraded

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Multiple Working Point Results

• Good behavior when using a single copy per round
• MWPnonstationarity is better than optimal
  nonstationary SWP BK98
• MWP is better with round stretching because it
  performs well even with small numbers of copies
  (and hardly needs stretching)

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Block Erasure Codes for Multislot Coding

• Message is partitioned into K fragments
• Encode into NgtK fragments
• Any K fragments suffice for decoding
• Modified performance measure
• Channel utilization instead of capacity
• Generation rate Sg of messages needs to be
  normalized by K

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Types of Multislot Coding

• Multiple round coding transmit several fragments
  of the code in each round
• Hybrid reservation coding in addition, once at
  least one fragment succeeds, the hub allocates
  channels for the remaining fragments

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Multiple Round Coding

• Transmit several fragments in each round
• The number of fragments transmitted depends on
• t - number of fragments previously transmitted
• k - number of fragments still required (out of K)
• d - number of rounds remaining till deadline
• Total number of fragments is fixed at Nmax

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Multiple Round Coding Mathematics

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Solution Dynamic Programming

• n(t,k,d) - number of copies to transmit in
  current round
• f(t,k,d) - mean number of fragments left to
  transmit, given (t,k,d)
• In last round, n(t,k,1)f(t,k,1)Nmax-t
• When dgt1, f(t,k,d) depends on n(t,k,d) and
  transmissions expected in following rounds

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Multiple Round Coding - Utilization
Ignoring increased header overhead
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Utilization Explanations

• Utilization approaches 1/e
• K - more fragments mean better utilization,
  but may increase header overheadPe - hard
  constraint means poor performance
• Dr - fewer rounds mean strict constraint
• Dividing the time slot by K gives time
  interpretation to Nmax/K

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Multiple Round Stretching
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Round Stretching Explanations

• Utilization approaches 1/e
• Time perspective
• Dr is unchanged
• Slots divided by K
• Number of slots per round increases
• Increasing K increases channel utilization,but
  may increase header overhead

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Other Classes of Multiple Round Coding

• General class of policies
• General function n(t,k,d)
• Stationary ammunition class
• Functions n(k,d) stationary of t
• Fixed-Nmax class sometimes transmits too much in
  the last round
• Stationary class uses reasonable budget in last
  round
• Utilization improvement for 3 rounds

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Hybrid Reservation Coding

• Initial coding phase - transmit several fragments
  of the code in each round
• Once (at least one) fragment succeeds, hub
  allocates channels for rest of fragments
• Policy divided into station-controlled coding
  phase, and hub-controlled reservation phase

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Different Types of Channels

• Coding phase requires channels
• Reservation phase requires ER channels
• The utilization can be bounded by
• One fragment succeeds in coding phase
• K-1 fragments via reservation
• Capacity bounded by

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Hybrid Reservation Coding Utilization
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Utilization Explanations

• Utilization approaches the bound
• Effects of K, Pe, and Dr similar to before
• Time interpretation of Nmax/K
• Amount transmitted in last round is either zero
  or significantly larger than K
• Much better than multiple round coding

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Hybrid Round Stretching
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Round Stretching Explanations

• Utilization approaches bound
• Time perspective as before
• Overhead reduces capacity
• Much better than multiple round coding

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Slot Length Considerations

• Packet lengths vary
• Minimizing internal fragmentation small slots
• Minimizing header overhead large slots
• Capacity reduction due to overhead
• This is offset by coding etc. (larger K)
• In any case, the new schemes bias optimal slot
  size in favor of smaller slots

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Multislot Coding Summary

• Large performance gains
• It works well for
• Small K
• Short delay constraints
• Round stretching
• Shortens optimal slot lengths

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Additional Issues

• Impure policies
• Same problem BK98
• Nondeterministic number of copies
• Negligible improvement
• Mean delay perspective

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Summary

• Single slot message
• Birk and Kerens results are good
• New techniques barely improve capacity
• Multislot problem
• Excellent results
• Effect on slot lengths

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Continuing Work

• Multislot Coding with MWP
• Optimized slot lengths
• Hybrid reservation with replication instead of
  coding