On a Property of the Soft Bit Density associated with Log- Likelihood Ratios of a Binary AWGN Channel
Conference: SCC'10 - 8th International ITG Conference on Source and Channel Coding
01/18/2010 - 01/21/2010 at Siegen, Germany
Pages: 6Language: englishTyp: PDFPersonal VDE Members are entitled to a 10% discount on this title
Rave, Wolfgang (Vodafone Chair Mobile Communications Systems, Technische UniversitÃ¤t Dresden, 01062 Dresden, Germany)
We derive a relation between the unconditional and conditional (conditioned on the input bit X to be either 0 or 1) densities of the expected bit value, the so-called â€™soft bitâ€™ Λ, given the log-likelihood ratios L(X) at the output of an AWGN channel. Both quantities are connected via the relation Λ = tanh(L/2). Denoting the unimodal, conditional soft bit density as f Λ|X,uni(λ|x) and the bimodal unconditional density as f Λ,bi(λ) we prove the following property: the mean of the conditional soft bit distribution is equal to the variance of the unconditional soft bit σ 2 Λ,bi, i.e. μ Λ|X,uni = σ 2 Λ,bi. This property is rooted in the consistency property of the associated L-value density.