Simple demo of FER improvement using Hamming (7,4) over a BSC

HamFER.jl

module HamFER

export run

using StaticArrays

const Gt = SA[1 0 0 0 ;
              0 1 0 0 ;
              0 0 1 0 ;
              0 0 0 1 ;
              1 1 1 0 ;
              0 1 1 1 ;
              1 0 1 1]

const epat = SA[1 0 0 0 ;
                0 1 0 0 ;
                0 0 1 0 ;
                0 0 0 1 ;
                0 0 0 0 ;
                0 0 0 0 ;
                0 0 0 0]

function encode(nibble::SVector{4,Int})::SVector{7,Int}
    return Gt*nibble .% 2
end

function iscodeword(cw::SVector{7,Int})::Bool
    if encode(cw[SVector(1,2,3,4)]) == cw
        return true
    end
    return false
end

function decode(rx::SVector{7,Int})::SVector{4,Int}
    idx_d = SVector(1,2,3,4)

    # If rx is a codeword, return it
    if iscodeword(rx)
        return rx[idx_d]
    end

    # Introduce 1-bit errors until a codeword is obtained
    for err in eachcol(epat)
        x = (rx .+ err) .% 2
        if iscodeword(x)
            return x[idx_d]
        end
    end

    # More than one error: bail out and return the data
    return rx[idx_d]
end

function BSC(b::Int, p::Float64)::Int
    if rand() < p
        return b+1 % 2
    else
        return b
    end
end

function run(; pb = 1e-3, experiments = 1000)
    idx_d = SVector(1,2,3,4)
    bsc(x) = BSC(x, pb)
    err_uncoded = 0 # errored frames without coding
    err_coded = 0   # errored frames with coding
    fer_uncoded = 0.0
    fer_coded = 0.0
    B = [0,1]

    # coded
    for i = 1:experiments
        for j = 1:16
            data = SVector{4}(rand(B, (4,)))
            cw = encode(data)
            rx = bsc.(cw)
            cw_est = decode(rx)
            if cw_est[idx_d] != data
                err_coded += 1
                break
            end
        end
    end

    # uncoded
    for i = 1:experiments
        data = SVector{64}(rand(B, (64,)))
        rx = bsc.(data)
        if data != rx
            err_uncoded += 1
        end
    end

    fer_coded = err_coded/experiments
    fer_uncoded = err_uncoded/experiments

    return (fer_uncoded, fer_coded,)
end

end