In this paper, lower bounds on error probability in coding for discrete classical and classical-quantum channels are studied. The contribution of the paper goes in two main directions: i) extending classical bounds of Shannon, Gallager and Berlekamp to classical-quantum channels, and ii) proposing a new framework for lower bounding the probability of error of channels with a zero-error capacity in the low rate region. The relation between these two problems is revealed by showing that Lovász' bound on zero-error capacity emerges as a natural consequence of the sphere packing bound once we move to the more general context of classical-quantum channels. A variation of Lovász' bound is then derived to lower bound the probability of error in the low rate region by means of auxiliary channels. As a result of this study, connections between the Lovász theta function, the expurgated bound of Gallager, the cutoff rate of a classical channel and the sphere packing bound for classical-quantum channels are established. Index TermsReliability function, sphere packing bound, Rényi divergence, quantum Chernoff bound, classical-quantum channels, Lovász theta function, cutoff rate.

We prove a new, improved upper bound on the size of codes C ⊆ {1, 2, 3, 4} n with the property that every four distinct codewords in C have a coordinate where they all differ. Specifically, we show that such a code has size at most 2 6n/19+o(n) , or equivalently has rate bounded by 6/19 ≤ 0.3158 (measured in bits). This improves the previous best upper bound of 0.3512 due to (Arikan 1994), which in turn improved the 0.375 bound that followed from general bounds for perfect hashing due to (Fredman and Komlós, 1984) and (Körner and Marton, 1988). The context for this problem is two-fold: zero-error list decoding capacity, where such codes give a way to communicate with no error on the "4/3 channel" when list-of-3 decoding is employed, and perfect hashing, where such codes give a perfect hash family of size n mapping C to {1, 2, 3, 4}.

The field of Distributed Video Coding (DVC) theory has received a lot of attention in recent years and effective encoding techniques have been proposed. In the present work the framework of pixel domain Wyner-Ziv coding of video frames is considered, following the scheme proposed in [1]. Some key frames are supposed to be available at the decoder while other frames are Wyner-Ziv encoded using turbo codes; at the decoder motion compensated interpolation between key frames is performed in order to construct the side information for the Wyner-Ziv frame decoding. In this paper an improved model for the correlation noise between the side information frame and the original one is proposed. It is shown that modeling nonstationary nature of the noise leads to substantial gain in rate-distortion performance. Also the memory of the noise is considered and the importance of placing an interleaver before the turbo code is shown as well.

Abstract-Let C(d) be the capacity of the binary deletion channel with deletion probability d.