Summary
This paper looks at how well pairs of codes can be used so that messages can be uniquely understood without confusion. The authors created a new example of such codes that work better than previous ones, and they also found an improved way to calculate the best possible performance. This helps to better understand the limits and possibilities when sending information using pairs of codes that do not get mixed up.
What this means in practice
- •For communication engineers: Design coding schemes for data transmission where uniquely decodable code pairs optimize transmission rates with provable upper bounds.
- •For error correction system designers: Develop error detection and decoding algorithms that use uniquely decodable code pairs with improved sum rate guarantees.
Abstract
We study the maximum sum rate of uniquely decodable code pairs. A weighted refinement of a complement-gluing construction yields an explicit code of length 672 and sum rate exceeding $1.318639029203$. An iterated projection argument, combined with a conditional entropy estimate and a justified continuous limit, gives an upper bound of $1.480063425539$.