We introduce TLHaar, an n-bit to n-bit reversible transform similar to the S-transform. TLHaar uses lookup tables that approximate the S-transform, but reorder the coefficients so they fit into n bits. TLHaar is suited for lossless compression in fixed-width channels, such as digital video channels and graphics hardware frame buffers. Tests indicate that when the incoming image data has lines or hard edges TLHaar coefficients compress better than S- transform coefficients. For other types of image data TLHaar coefficients compress up to 2.5% worse than those of the S-transform, depending on the data and the compression method used.

Arithmetic coding achieves a superior coding rate when encoding a binary source, but its lack of speed makes it an inferior choice when true high-performance encoding is needed. We present our work on a practical implementation of fast entropy coders for binary messages utilizing only bit shifts and table lookups. To limit code table size we limit our code lengths with a type of variable-to-variable (VV) length code created from source string merging. We refer to these codes as merged codes. With merged codes it is possible to achieve a desired level of speed by adjusting the number of bits read from the source at each step. The most efficient merged codes yield a coder with a worst-case inefficiency of 0.4%, relative to the Shannon entropy. Using a hybrid Golomb-VV Bin Coder we are able to achieve a compression ratio that is competitive with other state-of-the-art coders, at a superior throughput.

We introduce the Piecewise-Linear Haar (PLHaar) transform, a reversible n-bit to n-bit transform that is based on the Haar wavelet transform. PLHaar is continuous, while all current n-bit to n-bit methods are not, and is therefore uniquely usable with both lossy and lossless methods (e.g. image compression). PLHaar has both integer and continuous (i.e. non-discrete) forms. By keeping the coefficients to n bits PLHaar is particularly suited for use in hardware environments where channel width is limited, such as digital video channels and graphics hardware.