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In this paper we provide a method to obtain tight lower bounds on the minimum redundancy achievable by a Huffman code when the probability distribution underlying an alphabet is only partially known. In particular, we address the case where the occurrence probabilities are unknown for some of the symbols in an alphabet. Bounds can be obtained for alphabets of a given size, for alphabets of up to a given size, and for alphabets of arbitrary size. The method operates on a Computer Algebra System, yielding closed-form numbers for all results. Finally, we show the potential of the proposed method to shed some light on the structure of the minimum redundancy achievable by the Huffman code.

There is an increasing consumer demand for high bit-depth 4:4:4 HD video data playback due to its superior perceptual visual quality compared with standard 8-bit subsampled 4:2:0 video data. Due to vast file sizes and associated bitrates, it is desirable to compress raw high bit-depth 4:4:4 HD video sequences as much as possible without incurring a discernible decrease in visual quality. In this paper, we propose a Coding Block (CB)-level perceptual video coding technique for HEVC named Full Color Perceptual Quantization (FCPQ). FCPQ is designed to adjust the Quantization Parameter (QP) at the CB level (i.e., the luma CB and the chroma Cb and Cr CBs) according to the variances of pixel data in each CB. FCPQ is based on the default perceptual quantization method in HEVC called AdaptiveQP. AdaptiveQP adjusts the QP of an entire CU based only on the spatial activity of the constituent luma CB. As demonstrated in this paper, by not accounting for the spatial activity of the constituent chroma CBs, as is the case with AdaptiveQP, coding performance can be significantly affected; this is because the variance of pixel data in a luma CB is notably different from the variances of pixel data in chroma Cb and Cr CBs. FCPQ, therefore, addresses this problem. In terms of coding performance, FCPQ achieves BD-Rate improvements of up to 39.5% (Y), 16% (Cb) and 29.9% (Cr) compared with AdaptiveQP., Comment: Preprint: 2017 IEEE International Conference on Image Processing (ICIP 2017)

HEVC includes a Coding Unit (CU) level luminance-based perceptual quantization technique known as AdaptiveQP. AdaptiveQP perceptually adjusts the Quantization Parameter (QP) at the CU level based on the spatial activity of raw input video data in a luma Coding Block (CB). In this paper, we propose a novel cross-color channel adaptive quantization scheme which perceptually adjusts the CU level QP according to the spatial activity of raw input video data in the constituent luma and chroma CBs; i.e., the combined spatial activity across all three color channels (the Y, Cb and Cr channels). Our technique is evaluated in HM 16 with 4:4:4, 4:2:2 and 4:2:0 YCbCr JCT-VC test sequences. Both subjective and objective visual quality evaluations are undertaken during which we compare our method with AdaptiveQP. Our technique achieves considerable coding efficiency improvements, with maximum BD-Rate reductions of 15.9% (Y), 13.1% (Cr) and 16.1% (Cb) in addition to a maximum decoding time reduction of 11.0%., Comment: Data Compression Conference 2017