|Finite-Blocklength and Error-Exponent Analyses for LDPC Codes in Point-to-Point and Multiple Access Communication
|Yuxin Liu, Michelle Effros, California Institute of Technology, United States
|C.4: LDPC Codes
|Coding for Communications
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|This paper applies error-exponent and dispersion-style analyses to derive finite-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 bound achievable symmetrical and asymmetrical rates in the MAC. The dispersion-style analysis begins with a generalization of the random coding union (RCU) bound from random code ensembles with i.i.d. codewords to random code ensembles in which codewords may be statistically dependent; this generalization is useful since the codewords of random linear codes such as LDPC codes are dependent. Application of the RCU bound yields finite-blocklength error bounds and asymptotic achievability results for both i.i.d. random codes and LDPC codes. For discrete, memoryless channels, these results show that LDPC codes achieve first- and second-order performance that is optimal for the PPC and identical to the best prior results for the MAC.