New Counting Codes for Distributed Video Coding

TL;DR

This paper presents a novel counting code designed to enhance error correction in distributed video coding by maximizing Hamming distances between nearby codewords, thereby improving decoding accuracy.

Contribution

The paper introduces a new counting code derived from Gray Codes that increases Hamming distances between close codewords, aiding error correction in distributed video coding.

Findings

Significantly improves error correction in distributed video coding

Maximizes Hamming distance between adjacent and nearby codewords

Can be derived from Gray Codes for any bit depth

Abstract

This paper introduces a new counting code. Its design was motivated by distributed video coding where, for decoding, error correction methods are applied to improve predictions. Those error corrections sometimes fail which results in decoded values worse than the initial prediction. Our code exploits the fact that bit errors are relatively unlikely events: more than a few bit errors in a decoded pixel value are rare. With a carefully designed counting code combined with a prediction those bit errors can be corrected and sometimes the original pixel value recovered. The error correction improves significantly. Our new code not only maximizes the Hamming distance between adjacent (or "near 1") codewords but also between nearby (for example "near 2") codewords. This is why our code is significantly different from the well-known maximal counting sequences which have maximal average Hamming distance. Fortunately, the new counting code can be derived from Gray Codes for every code word length (i.e. bit depth).