# Free Ride on LDPC Coded Transmission

## TL;DR

This paper introduces the concept of accessible capacity to enable reliable superposition transmission of extra bits over existing coded links without additional energy or bandwidth, especially using LDPC codes.

## Contribution

It defines accessible capacity for practical channels, proposes superposition encoding and decoding methods, and demonstrates reliable transmission of up to 60 extra bits with LDPC codes.

## Key findings

- Up to 60 extra bits transmitted reliably with LDPC codes.
- Accessible capacity characterized as channel capacity minus payload mutual information.
- Superposition coding enables zero-cost additional data transmission.

## Abstract

In this paper, we formulate a new problem to cope with the transmission of extra bits over an existing coded transmission link (referred to as coded payload link) without any cost of extra transmission energy or extra bandwidth. This is possible since a gap to the channel capacity typically exists for a practical code. A new concept, termed as accessible capacity, is introduced to specify the maximum rate at which the superposition transmission of extra bits is reliable and has a negligible effect on the performance of the coded payload link. For a binary-input output-symmetric (BIOS) memoryless channel, the accessible capacity can be characterized as the difference between the channel capacity and the mutual information rate of the coded payload link, which can be numerically evaluated for very short payload codes. For a general payload code, we present a simple lower bound on the accessible capacity, given by the channel capacity minus the coding rate of the payload code. We then focus on the scenarios where low-density parity-check (LDPC) codes are implemented for the payload link. We propose to transmit extra bits by random superposition for encoding, and exhaustive search (with the aid of statistical learning) for decoding. We further propose, by establishing an auxiliary channel (called syndrome channel) induced from "zero-forcing" over the binary field, to transmit extra bits with structured codes such as repetition codes and first-order Reed-Muller (RM) codes. Numerical results show that up to 60 extra bits can be reliably transmitted along with a rate-1/2 LDPC code of length 8064.