Decoding algorithms with input quantization and maximum error correction capability

Decoding that uses soft-decision information but with multiple low-complexity decoders are investigated. These decoders correct only errors and erasures. The structure of the receiver consists of a bank of z demodulators followed by errors- and erasures-correcting decoders operating in parallel. Each demodulator has a threshold for determining when to erase a given symbol. We assign a cost f(θ) to the noise for causing an erasure when the receiver uses a particular threshold θ and a (larger) cost f(θ¯) for causing an error. The goal in designing the receiver is to choose the thresholds to maximize the noise cost which is necessary to cause a decoding error. We demonstrate that the above formulation is solvable for many channels including the M-ary input-output channel, the additive channel with coherent demodulation, and an additive channel with orthogonal modulation and noncoherent demodulation. Then we show that the maximum worst case error-correcting capability of the parallel decoding algorithms is the same as the maximum worst case error-correcting capability of a correlation decoder with the same number of quantization regions