On upper bounds for the achievable rates of LDPC codes

Upper bounds on the mutual entropy of syndrome components of low-density parity-check (LDPC) codes are developed. Using these bounds, an upper bound is derived on the rates of LDPC codes for which reliable communication over a memoryless binary-input symmetric-output (MBIOS) channel is achievable. This bound improves on the earlier known bounds due to Gallager, Burshtein et al., and Weichmann-Sason.