Coding-theory results from MacKay

BoundedDistanceNoise: Shannon versus bounded-distance noise limits of a rate-R code. SelfDualCodeCheck: is G = (I | t(P)) self-dual (P orthogonal mod 2). RunlengthCapacity: capacity of the channel forbidding runs of more than L ones. RepetitionErrorApprox: leading-order repetition-code error. RobustSoliton: Luby's robust soliton degree distribution. CodeLengthDecomposition: L = H + KL - log2 z. McGillInteractionInformation: I(X;Y|Z) - I(X;Y). Identical to the Python arm morie.fn.infocodes.

Usage

BoundedDistanceNoise(rate)

SelfDualCodeCheck(P)

RunlengthCapacity(L)

RepetitionErrorApprox(N, f, target = NULL)

RobustSoliton(K, c = 0.1, delta = 0.5)

CodeLengthDecomposition(p, lengths)

McGillInteractionInformation(pxyz)

Arguments

rate

Code rate in (0, 1).

P

K by K binary matrix.

L

Maximum run length.

N

Blocklength (odd).

f

Bit-flip probability in (0, 1/2).

target

Optional target error probability.

K

Number of source packets.

c, delta

Robust soliton constants.

p

Symbol probabilities.

lengths

Codeword lengths.

pxyz

Three-way array of joint probabilities or counts.

Value

List.

References

MacKay, D. J. C. (2003). Information Theory, Inference, and Learning Algorithms. Cambridge University Press.

Luby, M. (2002). LT codes. Proceedings of the 43rd IEEE Symposium on Foundations of Computer Science, 271-280.

McGill, W. J. (1954). Multivariate information transmission. Psychometrika 19, 97-116.

Examples

BoundedDistanceNoise(0.5)
#> $f_shannon
#> [1] 0.1100279
#> 
#> $f_bd
#> [1] 0.05501393
#> 
RobustSoliton(10000, 0.2, 0.05)$S
#> [1] 244.1215
CodeLengthDecomposition(c(0.5, 0.25, 0.125, 0.125), c(1, 2, 3, 3))$L
#> [1] 1.75