For a new discrete soft-decision channel with linearly ordered reliabilities, the paper derives closed-form error and success exponents for random-code ML decoding and proves soft-decision decoding strictly outperforms hard-decision decoding.
Gallager,Principles of Digital Communication
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The Linear Reliability Channel
For a new discrete soft-decision channel with linearly ordered reliabilities, the paper derives closed-form error and success exponents for random-code ML decoding and proves soft-decision decoding strictly outperforms hard-decision decoding.