Source Coding with Causal Side Information at the Decoder

摘要

Consider the following problem of source coding with causal side information at the decoder. The source and side information are generated as independent drawings (X_i, Y_i) of the pair (X, Y) ～ p(x,y). Encoding is performed by mapping the sequence X~n into T ∈ {1..., [2~(nR)] }. The i-th reconstruction is of the form X_i(T, Y~i), i.e., it is allowed to depend on the side information, but only causally. The motivation for studying this problem comes from source coding systems that are constrained to operate with no, or with limited, delay. Sequential source codes with a limited-delay encoder and a sequential, zero-delay, decoder with access to side information comprise a subfamily of the schemes that our notion of causal decoder side information allows, since our formulation does not limit the encoding delay. In particular, our formulation encompasses "real-time Wyner Ziv" coding schemes, as recently introduced in [8]. Consequently, our negative (converse) results immediately apply to all such source coding scenarios. On the positive side, as we show, in some cases, schemes from the more limited (and realistic) family of "real-time" codes can achieve optimum performance within the larger family that we allow.