polar codes over wireless fading channels n.
Download
Skip this Video
Loading SlideShow in 5 Seconds..
Polar Codes over Wireless Fading Channels PowerPoint Presentation
Download Presentation
Polar Codes over Wireless Fading Channels

Loading in 2 Seconds...

play fullscreen
1 / 17

Polar Codes over Wireless Fading Channels - PowerPoint PPT Presentation


  • 344 Views
  • Uploaded on

Polar Codes over Wireless Fading Channels. Siddharth Dangi Arjun Singh. Polar codes. Introduced by Erdal Arikan Achieve the symmetric capacity of any binary-input discrete memoryless channel (B-DMC) examples of B-DMCs: BEC, BSC Complexity O(N log N) for both encoder and decoder.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'Polar Codes over Wireless Fading Channels' - kennan-faulkner


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
polar codes
Polar codes
  • Introduced by Erdal Arikan
  • Achieve the symmetric capacity of any binary-input discrete memoryless channel (B-DMC)
    • examples of B-DMCs: BEC, BSC
  • Complexity O(N log N) for both encoder and decoder
channel polarization
Channel polarization
  • start with
    • N independent and identical B-DMCs with symmetric capacity C
  • end up with (for large N)
    • NC channels with symmetric capacity ≈ 1
    • N(1-C) channels with symmetric capacity ≈ 0
  • Send data through channels with capacity ≈ 1
application to wireless channels
Application to wireless channels
  • Idea – model the channel as BSEC (“binary symmetric erasure channel”)
    • declare deep fades as erasures
    • other error events cause bit flips
  • N channels are:
    • in time, across N symbol times
    • in frequency, across N OFDM subcarriers
notation terminology
Notation & Terminology
  • W – a B-DMC with input x and output y
  • W(y|x) – transition probability
  • “symmetric capacity” (rate)
    • highest rate achievable using input symbols with equal frequency
  • “Bhattacharyya parameter” (reliability)
polar encoder general
Polar Encoder (general)
  • block length N = 2n
  • 3 stages of WN
    • form s from u
    • “reverse shuffle”
    • 2 N/2 polar encoders
  • linear operation!
polar encoder
Polar Encoder
  • matrix representation:
  • matrix for N = 4
  • depending on rate R, fix some positions of u
  • example: “freeze” indices 1 and 3 (R = ½)
polar decoder
Polar Decoder
  • successive cancellation (SC) decoder

for i = 1,…,N generate decision for bit i based on: 1. received bits y1,…, yN 2. decisions for bits 1,…,i-1end

  • suboptimal, but leads to efficient recursive computation for decision functions
    • can still achieve symmetric capacity
choosing frozen set
Choosing Frozen Set
  • choose indices for which corresponding “new” channels have either the
    • highest symmetric capacities (closest to 1)
    • lowest Bhattacharyya parameters (closest to 0)
  • both methods achieve symmetric capacity
  • second method gives explicit bound:
calculating bhattacharyya parameters
Calculating Bhattacharyya parameters
  • nice recursive formulas if W is a BEC
  • for other channels, can use approximation:
    • calculate symmetric capacity C of W
    • approx. W as a BEC with erasure probability 1 – C
    • use BEC recursive formulas
simulation parameters
Simulation parameters
  • Rayleigh fading channel
    • 2 paths
    • Td = 10 μs
    • DS = 100 Hz
  • OFDM
    • QPSK modulation
    • W = 1.25 MHz
    • NC = 128
implementation issues
Implementation issues
  • Decoding in MATLAB too slow for large N
  • Repeated computation in recursive formulas for SC decoder
  • Underflow in computation of likelihood ratios for large N