The likelihood encoder for lossy source compression

Abstract

Abstract-In this work, a likelihood encoder is studied in the context of lossy source compression. The analysis of the likelihood encoder is based on a soft-covering lemma. It is demonstrated that the use of a likelihood encoder together with the soft-covering lemma gives alternative achievability proofs for classical source coding problems. The case of the rate-distortion function with side information at the decoder (i.e. the Wyner-Ziv problem) is carefully examined and an application of the likelihood encoder to the multi-terminal source coding inner bound (i.e. the BergerTung region) is outlined.

The Henchman Problem: Measuring Secrecy by the Minimum Distortion in a List

“…For the entirety of the proof, we use the henchman formulation instead of the list reconstruction one. The main idea in the proof of achievability concerns the problem of compressing codewords from a random codebook beyond the rate-distortion limit; the proof also relies on a likelihood encoder [6] and the soft covering lemma [7, Lemma IV.1]. The converse is straightforward, as we now show.…”

“…We now complete the proof of achievability by showing that the likelihood encoder can be used to achieve distortion E d B (X, Y ) at the legitimate receiver (this is also done in [6]). To do this, Node B uses a deterministic decoder that simply produces the codeword indexed by (m, k), i.e., P Y n |M K (y n |m, k) = 1{y n = y n (m, k)}.…”

“…The likelihood encoder of [6] for lossless reconstruction and for this codebook is a stochastic encoder defined by…”

“…As detailed in [6], a likelihood encoder is a particular stochastic encoder which, when combined with a random codebook, manages to avoid many of the tedious and technical components of achievability proofs in lossy compression problems. The primary conduit for the analysis of a likelihood encoder is the "soft covering lemma", which is expounded upon in [7].…”

Resolvability in E<inf>&#x03B3;</inf> with applications to lossy compression and wiretap channels

“…Remark 7. Since the E γ metric reduces to TV when γ = 1, Theorem 5 generalizes the likelihood source encoder based on the standard soft-covering/resolvability lemma [8]. In [8], the error exponent for the likelihood source encoder at rates above the rate-distortion function is analyzed using the exponential decay of TV in the approximation of output statistics, and the exponent does not match the optimal exponent in [13].…”