Error Exponents of LDPC Codes under Low-Complexity Decoding

Abstract

This paper deals with the specific construction of binary low-density parity-check (LDPC) codes. We derive lower bounds on the error exponents for these codes transmitted over the memoryless binary symmetric channel (BSC) for both the well-known maximum-likelihood (ML) and proposed low-complexity decoding algorithms. We prove the existence of such LDPC codes that the probability of erroneous decoding decreases exponentially with the growth of the code length while keeping coding rates below the corresponding channel capacity. We also show that an obtained error exponent lower bound under ML decoding almost coincide with the error exponents of good linear codes.

Keywords

• low-density parity check (LDPC) codes
• Gallager’s LDPC codes
• binary LDPC codes
• decoding algorithm
• low-complexity
• error exponent