# Two-Dimensional Source Coding by Means of Subblock Enumeration

## TL;DR

This paper extends the substring enumeration compression technique to two-dimensional sources like images by introducing a block-based approach using a flat torus model, reducing complexity and analyzing code length limits.

## Contribution

It proposes a new 2D source coding method using block-by-block encoding with a flat torus model, improving efficiency over line-by-line methods.

## Key findings

- Reduces encoding complexity for 2D sources
- Uses flat torus as a probabilistic model
- Analyzes average codeword length limits

## Abstract

A technique of lossless compression via substring enumeration (CSE) attains compression ratios as well as popular lossless compressors for one-dimensional (1D) sources. The CSE utilizes a probabilistic model built from the circular string of an input source for encoding the source.The CSE is applicable to two-dimensional (2D) sources such as images by dealing with a line of pixels of 2D source as a symbol of an extended alphabet. At the initial step of the CSE encoding process, we need to output the number of occurrences of all symbols of the extended alphabet, so that the time complexity increase exponentially when the size of source becomes large. To reduce the time complexity, we propose a new CSE which can encode a 2D source in block-by-block instead of line-by-line. The proposed CSE utilizes the flat torus of an input 2D source as a probabilistic model for encoding the source instead of the circular string of the source. Moreover, we analyze the limit of the average codeword length of the proposed CSE for general sources.