## 1 Introduction  
Steganography is a technique used for covert communication, where confidential information is hidden within multimedia carriers such as image [1, 2], text [3, 4], video [5, 6], and audio [7, 8] files without arousing suspicion. While steganography can serve legitimate purposes in protecting sensitive information, it is essential to recognize that it can also be misused for illegal activities, including terrorism. To counteract the potential misuse of steganography, the development of steganalysis [9, 10] methods becomes crucial. Steganalysis refers to the field of study dedicated to detecting and analyzing hidden information within multimedia carriers. Indeed, network streaming media services [11] have experienced a significant surge in popularity in recent years. This can be attributed to the growing demand for higher bandwidth and the convergence of networks. In this context, low-bit-rate compressed speech codecs have emerged as a preferred choice for these streaming media services due to their efficient performance. Low-bit-rate speech codecs [11, 12] are designed to compress speech signals while maintaining an acceptable level of quality. Due to their efficient compression and satisfactory quality, low-bit-rate voice streams have become a relatively optimal carrier for embedding secret information. Existing steganography techniques for low-bit-rate speech streams include approaches such as cochlear delay-based methods [13], spread spectrum-based methods [14], least significant bit (LSB) modification-based methods [15, 16], and quantization index modulation (QIM)-based methods [17, 18, 19, 20, 21]. Cochlear delay-based methods exploit perceptual models of human auditory processing by modifying temporal characteristics such as inter-channel or inter-frame delays to embed information. Spread-spectrum-based methods [14] embed secret information by spreading it across a wide frequency band within the host signal. In the LSB approach [15, 16], the values of certain code elements are directly manipulated to embed secret information. By altering the least significant bits of selected elements, hidden data can be inserted into the speech stream. This approach is relatively simple to implement and generally maintains the perceptual quality of the speech signal. However, LSB-based methods are typically very fragile and vulnerable to both intentional and unintentional modifications, making them less robust against steganalysis and signal-processing attacks. QIM-based steganography methods [17, 18, 19, 20, 21] utilize quantization index modulation to embed data by carefully modifying the search space of vector quantization (VQ) codewords during the encoding process. QIM-based approaches are designed to balance the trade-offs among distortion, robustness, and embedding capacity, making them particularly suitable for low-bit-rate speech codecs [22]. Although all four types of techniques have been explored in the literature, QIM-based steganography generally offers superior trade-offs in terms of imperceptibility, robustness, and compatibility with existing codecs. Consequently, most recent research on steganalysis in low-bit-rate speech coding has focused on detecting QIM-based methods. Accordingly, our work is dedicated to addressing the challenges of frame-wise detection for QIM-based steganography in low-bit-rate speech streams. To detect QIM-based steganography techniques [17, 18, 19, 20, 21], existing steganalysis methods [21, 23, 24, 25, 26, 27, 28, 29, 30, 31] can be categorized into two types. The first type [24, 25, 26, 32] involves utilizing the statistical characteristics of the codeword distribution to extract steganalysis features. Common statistical characteristics used include the Markov transition matrix [24, 32], entropy, and conditional probability. These features are employed to analyze the presence of hidden information in the speech stream.