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This paper applies error-exponent and dispersion-style analyses to derivefinite-blocklength achievability bounds for low-density parity-check (LDPC)codes over the point-to-point channel (PPC) and multiple access channel (MAC).The error-exponent analysis applies Gallager's error exponent to boundachievable symmetrical and asymmetrical rates in the MAC. The dispersion-styleanalysis begins with a generalization of the random coding union (RCU) boundfrom random code ensembles with i.i.d. codewords to random code ensembles inwhich codewords may be statistically dependent; this generalization is usefulsince the codewords of random linear codes such as random LDPC codes aredependent. Application of the RCU bound yields improved finite-blocklengtherror bounds and asymptotic achievability results for i.i.d. random codes andnew finite-blocklength error bounds and achievability results for LDPC codes.For discrete, memoryless channels, these results show that LDPC codes achievefirst- and second-order performance that is optimal for the PPC and identicalto the best-prior results for the MAC.

Finite-Blocklength and Error-Exponent Analyses for LDPC Codes in Point-to-Point and Multiple Access Communication