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sbates130272/sdc_ecc.m

Created September 19, 2017 01:51
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  1. sbates130272 created this gist Sep 19, 2017.
    104 changes: 104 additions & 0 deletions sdc_ecc.m
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    ## Copyright (C) 2017 Stephen Bates
    ##
    ## This program is free software; you can redistribute it and/or modify it
    ## under the terms of the GNU General Public License as published by
    ## the Free Software Foundation; either version 3 of the License, or
    ## (at your option) any later version.
    ##
    ## This program is distributed in the hope that it will be useful,
    ## but WITHOUT ANY WARRANTY; without even the implied warranty of
    ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
    ## GNU General Public License for more details.
    ##
    ## You should have received a copy of the GNU General Public License
    ## along with this program. If not, see <http://www.gnu.org/licenses/>.

    ## Author: Stephen Bates <batesste@ennis.local>
    ## Created: 2017-08-20

    ##
    ## sdc_ecc.m
    ## ---------
    ##
    ## This simple script generates the "Bates Conjecture" curve that shows what
    ## the media Raw Bit Error Rate (RBER) needs to be to reach a target
    ## Uncorrectable Bit Error Rate (UBER) as specified by the user.
    ##
    ## Basically the code works by assuming a constant code rate (eCodeRate) across
    ## a range of ECC codeword sizes and determines (via a simple binary search) the
    ## media RBER needed to target the provided UBER. We assume ECC is done via
    ## a Hamming code type structure and the symbol size and correction capabilities
    ## are computed accordingly.

    close all; clear all; clc

    eCodeRate = 0.9; # Code rate, should be between 0 and 1.
    eStartBer = 1e-3; # The start RBER for the binary search
    eUber = 1e-18; # The target UBER.
    pnN = 64:32:8*4096;
    # The ECC codeword sizes to compute over


    # Calculate the K, M and T for the ECC codewords based on Hamming code
    # type assumptions.

    pnK = floor(eCodeRate*pnN);
    pnM = floor(log2(pnN));
    pnT = floor((pnN.-pnK)./pnM);

    # Now we enter a search loop for each ECC codeword size using the
    # incremental Beta function to determine what RBER results in the target
    # UBER for that size. Stop when we get within 1% of eUber.

    peProbFecError = [];
    peInputBer = [];

    for i=1:length(pnT)

    eOutputBer = 0.5;
    eInputBer = 24/1080/8;
    bGoingDown = true;
    eScale = 0.5;
    eTol = 0.01;
    bUseFer = true;

    while abs((eOutputBer-eUber)/eUber)>eTol

    eOutputFer = betainc(eInputBer, pnT(i)+1, pnN(i)-pnT(i)-1);

    if bUseFer
    eOutputBer = eOutputFer;
    end

    if eOutputBer>eUber
    if ~bGoingDown
    eScale = (1+eScale)/2;
    eScale = 1/eScale;
    bGoingDown = true;
    end
    eInputBer = eInputBer*eScale;
    else
    if bGoingDown
    eScale = (1+eScale)/2;
    eScale = 1/eScale;
    bGoingDown = false;
    end
    eInputBer = eInputBer*eScale;
    end
    end

    peInputBer = [ peInputBer eInputBer ];


    end

    # Plot the results with Bytes as the X-Axis. Also save to a PNG (this line
    # works in Octave by might break Matlab).

    figErr = figure();
    hold on ; grid on ; zoom on
    loglog(pnN./8, peInputBer);
    ylabel('Required Media RBER')
    xlabel('Media Codeword Size (Bytes)')
    title('Media RBER vs Codeword Size for 1e-18 UBER')
    print(figErr,"sdc_ecc.png","-dpng");