Coded Computation Against Straggling Channel Decoders In The Cloud - - PowerPoint PPT Presentation

Coded Computation Against Straggling Channel Decoders In The Cloud For Gaussian Channels

Jinwen Shi, Cong Ling (speaker), Imperial College London Osvaldo Simeone, King's College London Jörg Kliewer, New Jersey Institute of Technology

Special thanks go to everyone

ISIT 2020 Worldwide

Background

¨ M. Aliasgari, J. Kliewer and O.

Simeone, “Coded computation against processing delays for virtualized cloud-based channel decoding,” 2017 (T-COM 2019). Considered binary-symmetric channels (BSC) and binary codes.

¨ Imperial College group

worked on lattice codes.

¨ Natural to extend to

Gaussian channels.

• Paper submitted to a conference in 2018 but

for no reasons (i.e., no review).

• Accepted by ISIT 2020!

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System model (uplink)

BSC channel, (Aliasgari, Kliewer, Simeone’17)

• Cloud radio access network (C-RAN) with distributed decoding.
• To handle straggling processors, Cloud re-encodes received packets.

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RRH: remote radio head NFV: network function virtualization

Motivation

q Trivial extension? q Not really. q BSC: no “combining

gain” from binary codes.

q Gaussian channel: can

we exploit “combining gain” by lattice codes?

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Modified compute-and-forward on the cloud

¨ Compute-and-forward

(Nazer, Gastpar’11):

packets naturally combined by the channel

¨ Our work:

packets artificially combined by the cloud

• Difference: accumulated noise
• Also makes noise terms correlated at different servers

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Encoding

¨ (Single) User ¤ file is divided into K

blocks;

¤ each block Î Fp

k is

encoded using a lattice code of length n and rate R;

¤ blocks received by remote

radio heads (RRH)

¨ Cloud ¤ network function

virtualization (NFV) encoder re-encodes K packets into N blocks, using an (N,K) linear code with generator matrix Gc

¤ N servers with random

delays

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Two types of codes

¨ Lattice code

¤ User ¤ Channel coding ¤ Assuming capacity-

achieving nested lattice codes (Erez-Zamir’05)

¨ NFV code

¤ Cloud ¤ Packet error/erasure

correction code

¤ Deal with straggling

processors

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Lattice decoding

¨ Re-encoded packets ¨ Server i gets block ¨ and aims to decode a linear equation using lattice

decoding

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Computation rate

¨ Main Theorem: Transmission rate that allows

reliable decoding of a given equation

¨ Rate penalty = (column norm) due to

noise accumulation.

¨ (Non-binary) NFV codes with binary/sparse

generator matrices appear to be better.

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Error probability

¨ Under ML lattice decoding

¤

is the Poltyrev random coding exponent

¤

where D is the gap to computational rate

¨ Plugged into (Aliasgari, Kliewer, Simeone’17) to obtain

bounds on packet/frame error probability (FER)

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Numerical results

¨ Firstly, no NFV

coding, only parallel processing

¨ LDB: large

deviation bound

¨ UB: Union bound

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Numerical results

¤ Then, comparison of

different encoding schemes

¤ NFV code (dmin = 3)

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Concluding remarks

¨ Have we achieved our

goal set initially against BSCs?

¨ Have to tolerate some

rate loss to cope with straggling decoders.

¨ Need NFV codes with

sparse/binary generator matrices and good error correction.

¨ Simulation with

practical lattice codes.

¨ From a single-user

model to multi-user uplink model.

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Support from EPSRC, ERC and NSF is acknowledged Email: cling@ic.ac.uk

Thanks for your attention!

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