## 1 Introduction  
Channel coding, applied to reduce the errors in transmissions, is an important part in digital communications [1]. The binary Bose-Chaudhuri-Hocquenghem (BCH) codes are widely used for their powerful error-correcting capability [2], convenient design of encoders [3], and efficiency of decoding algorithms [4, 5]. In traditional communication systems, the coding parameters are known by both the transmitters and receivers, but with the development of cognitive radios and intelligent techniques, blind recognition of the channel coding parameters is becoming available and realizable. Cognitive radio (CR) was introduced in [6] as a smart spectrum sharing technology, and it is becoming a hot research topic [7, 8, 9, 10]. The adaptive coding and modulations (ACM) technique [11, 12, 13, 14] is an important section of the CR to adapt the channel. In an ACM system, the transmitter chooses optimized coding and modulation parameters according to the channel quality. Thus at the reception, the receiver need to recognize those parameters before demodulation and decoding. Another application field of the blind recognition technique is non-cooperative communications [15, 16]. In this case, a non-cooperative receiver does not known the modulation and coding parameters before recognizing them. In the future communications, the terminals are required to be as intelligent as possible to adapt themselves to a specific context and to blindly estimate the transmitter parameters for self-reconfiguration purpose, only with knowledge of the received data stream [17]. To the best of our knowledge, most of the blind recognition algorithms proposed in the literature are focused on convolutional codes. In [18], a Euclidean-algorithm-based method was proposed to identify a 1/2 rate convolutional encoder in noiseless cases. However, it is not suitable for noisy channels. In [19], another approach was presented to identify a 1/n rate convolutional encoder in noisy cases based on the Expectation Maximization algorithm. The authors of [20, 21] developed methods for blind recovery of convolutional encoders in turbo code configuration. In [13] and [17], dual code methods for blind identification of k/n rate convolutional codes ware proposed for cognitive radio receivers. In this paper we consider the problem of blind recognition of the coding parameters for a cognitive receiver. The main focus is on the widely used BCH codes. Some previous literature reports [22, 23, 24] proposed and developed recognition algorithms for BCH codes in hard decision situations. In [22] and [23], the authors proposed a blind recognition algorithm for BCH codes based on Root Information Dispersion Entropy and Root Statistic (RIDERS). This algorithm can achieve correct recognition with a bit error rate (BER) of \(10^{-2}\), but it is computationally intensive, especially when the code length is large. The authors of [24] improved that algorithm proposed in [22, 23] to reduce the computational complexity, which made the recognition procedure faster. However, the previous works on blind recognition of BCH codes are all in hard decision situations, and are based on utilizing the algebraic properties of the codes in Galois Fields (GF). To achieve available recognition results, large amounts of training data are always required. With the development of sampling and signal processing techniques, the soft output of the channel has become available. Many soft-decision-based decoding algorithms have been applied to the error-correcting codes [25, 26, 27, 28, 29, 30] and yield better decoding performances than hard decision algorithms. Some blind frame synchronization techniques for error correcting codes also utilize the soft output of the channel to improve the synchronization performances [31, 32, 33, 34]. Inspired by the soft decision decoding algorithms, we develop theRIDERS algorithm introduced by [22; 23; 24] in the soft decision situations in this paper. As an example we mainly discuss the problem of the soft decisions of BPSK modulation on AWGN channels.