Low Density Parity Check Codes

• Introduction
  • Constructing LDPC Codes
    • LDPCCode(H): MtrxSprs → Code
    • GallagerCode(n, a, b): RngIntElt, RngIntElt, RngIntElt → Code
    • RegularLDPCEnsemble(n, a, b): RngIntElt, RngIntElt, RngIntElt → Code
    • IrregularLDPCEnsemble(n, Sc, Sv): RngIntElt, SeqEnum, SeqEnum → Code
    • MargulisCode(p): RngIntElt → Code
    • Example: Is LDPC
  • Access Functions
    • IsLDPC(C): Code → BoolElt
    • AssignLDPCMatrix(~C, H): Code, MtrxSprs
    • LDPCMatrix(C): Code → MtrxSprs
    • LDPCDensity(C): Code → FldReElt
    • IsRegularLDPC(C): Code → BoolElt
    • TannerGraph(C): Code → Grph
    • LDPCGirth(C): Code → RngIntElt
    • LDPCEnsembleRate(v, c): RngIntElt, RngIntElt → FldReElt
    • LDPCEnsembleRate(Sv, Sc): [FldReElt], [FldReElt] → FldReElt
    • Example: Is LDPC
  • LDPC Decoding and Simulation
    • LDPCDecode(C, v): Code, ModTupRngElt → ModTupRngElt
    • Example: DecodeLDPC BSC
    • Example: DecodeLDPC BSC
    • LDPCSimulate(C, N): Code, RngIntElt → FldReElt, FldReElt
    • Example: Decode Ensemble
  • Density Evolution
    • LDPCBinarySymmetricThreshold(v, c): RngIntElt, RngIntElt → FldReElt
    • LDPCBinarySymmetricThreshold(Sv, Sc): [FldReElt], [FldReElt] → FldReElt
    • DensityEvolutionBinarySymmetric(v, c, p): RngIntElt, RngIntElt, FldReElt → BoolElt
    • DensityEvolutionBinarySymmetric(Sv, Sc, p): [FldReElt], [FldReElt], FldReElt → BoolElt
    • Example: DE BSC
    • LDPCGaussianThreshold(v, c): RngIntElt, RngIntElt → FldReElt
    • LDPCGaussianThreshold(Sv, Sc): [FldReElt], [FldReElt] → FldReElt
    • DensityEvolutionGaussian(v, c, σ): RngIntElt, RngIntElt, FldReElt → BoolElt
    • DensityEvolutionGaussian(Sv, Sc, σ): [FldReElt], [FldReElt], FldReElt → BoolElt
    • GoodLDPCEnsemble(i): RngIntElt → FldReElt, [FldReElt], [FldReElt]
    • Example: DE Gaussian