# Construction of Unrestricted Rate Parallel Random Input Output Code

## TL;DR

This paper proposes a new coding scheme for two-page unrestricted-rate PRIO codes with different rates, achieving higher sum rates and guaranteeing unique decodability through a constructive approach.

## Contribution

It introduces a novel two-page coding scheme with disjoint codes, improving sum rates and providing a constructive method for arbitrary code lengths.

## Key findings

- Higher sum rates than previous codes
- Disjoint codes constructed using constant-weight code principles
- Constructive scheme applicable to arbitrary code lengths

## Abstract

A coding scheme for two-page unrestricted-rate PRIO code that each page may have different code rates is proposed. In the second page, the code for each messages consists of two complementary codewords with code length n. There are a total of 2n-1 codes which are disjoint to guarantees uniquely decodable for 2n-1 messages. In the first page, the code for each message consists of all weight-u vectors with their non-zero elements restricted to (2u-1) same positions, where non-negative integer u is less than or equal to half of code length. Finding codes to be disjoint in first page is equivalent to construction of constant-weight codes, and the numbers of disjoint codes are the best-known numbers of codewords in constant-weight codes. Our coding scheme is constructive, and the code length is arbitrary.The sum rates of our proposed codes are higher than those of previous work.