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# Communications in Information and Systems

## Volume 16 (2016)

### Number 2

### A randomized covering-packing duality between source and channel coding

Pages: 83 – 109

DOI: http://dx.doi.org/10.4310/CIS.2016.v16.n2.a1

#### Authors

#### Abstract

Let $b$ be a *general channel*, defined as a sequence of transition probabilities in the sense of Verdu and Han, over which the uniform $X$ source, denoted by $U$, is *directly* communicated to within distortion level $D$. The source $U$ puts uniform distribution on all sequences with type *precisely* $p_X$ as compared with the i.i.d. $X$ source which puts ‘most of’ its mass on sequences with type ‘close to’ $p_X$. A *randomized* covering-packing duality is established between source-coding and channel-coding by considering the source-coding problem (covering problem) of coding the source $U$ to within distortion level $D$ and the channel coding problem (packing problem) of reliable communication over $b$, thus leading to a proof of $C \geq R_U (D)$ where $C$ is the capacity of $b$ and $R_U (D)$ is the rate-distortion function of $U$. This also leads to an operational view of source-channel separation for communication with a fidelity criterion.