An Embedding Strategy Using Q-Ary Convolutional Codes for Large and Small Payloads

Jyun-Jie Wang,Hsi-Yuan Chang,Sheng-Chih Yang,Yin-Chen Lin,Chi-Yuan Lin

doi:10.3390/math9131577

Jyun-Jie Wang, Hsi-Yuan Chang + Show 3 more

Open Access

https://doi.org/10.3390/math9131577

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Abstract

Matrix embedding (ME) code is a commonly used steganography technique, which uses linear block codes to improve embedding efficiency. However, its main disadvantage is the inability to perform maximum likelihood decoding due to the high complexity of decoding large ME codes. As such, it is difficult to improve the embedding efficiency. The proposed q-ary embedding code can provide excellent embedding efficiency and is suitable for various embedding rates (large and small payloads). This article discusses that by using perforation technology, a convolutional code with a high embedding rate can be easily converted into a convolutional code with a low embedding rate. By keeping the embedding rate of the (2, 1) convolutional code unchanged, convolutional codes with different embedding rates can be designed through puncturing.

Highlights

Among the numerous steganography techniques that have been developed, matrix embedding (ME) [1,2] provides high undetectability and embedding efficiency, which result in efficient steganographic security
Numerous ME codes based on covering codes [3,4,5,6] have been developed because they exhibit high embedding efficiency due to their favorable structural characteristics, such as excellent weight distribution of the coset leaders of linear codes
Constructing a structured q-ary convolutional embedding (CE) code with embedding efficiency close to the theoretical limit is a key open problem, involving the following aspects: (1) the embedding scheme requires a structured code of sufficient length, and must have an excellent parity check matrix or generator matrix; (2) the structured code is computationally efficien10t,oafn12d an effective encoding/decoding process has been developed based on the structured code

Summary

Introduction

Among the numerous steganography techniques that have been developed, matrix embedding (ME) [1,2] provides high undetectability and embedding efficiency, which result in efficient steganographic security. Numerous ME codes based on covering codes [3,4,5,6] have been developed because they exhibit high embedding efficiency due to their favorable structural characteristics, such as excellent weight distribution of the coset leaders of linear codes. The technique exhibited high efficiency for large payloads [7], which resulted in superior steganographic security They use structured simple codes (including decoding by using fast Hadamard decoding) to obtain effective ME codes and approach the efficiency limit of large payloads. The best ME code (ME code that can approach the upper limit of the embedding efficiency of the rate-distortion function) requires a well-structured code and a sufficiently long effective decoding algorithm, such as a low-density generator matrix code [14].

Cover for multitone images

Embedding Algorithm for Small and Large Payloads

Optimal Design for Q-Ary CEs

Conclusions