A novel algorithm of blind recognition of Bose-Chaudhuri-Hocquenghem (BCH) codes is proposed to solve the problem of Adaptive Coding and Modulation (ACM) in cognitive radio systems. The recognition algorithm is based on soft decision situations. The code length is firstly estimated by comparing the Log-Likelihood Ratios (LLRs) of the syndromes, which are obtained according to the minimum binary parity check matrixes of different primitive polynomials. After that, by comparing the LLRs of different minimum polynomials, the code roots and generator polynomial are reconstructed. When comparing with some previous approaches, our algorithm yields better performance even on very low Signal-Noise-Ratios (SNRs) with lower calculation complexity. Simulation results show the efficiency of the proposed algorithm.

Adaptive Coding and Modulation (ACM) technique is one of the most important techniques of cognitive radio networks for the intelligent communications [

An intelligent communication system.

In this paper, we consider the problem of blind identification of channel coding parameters for the intelligent communication systems which use binary BCH codes. We assume that the estimation of signal power and modulation mode is achieved. The transmitters might choose the optimized code length and code rate according to the channel conditions to get the best balance between information transmission speed and fault tolerance. But the receivers always could not get the channel coding parameters directly. In [^{−2}, but the calculation complexity is large, especially when the code length is long. The authors of [

In this paper, we propose a new algorithm to recognize the BCH codes parameters for the soft decision situations. Although the previous works have good performance, the main base of those algorithms is utilizing the algebraic properties of the codes in Galois Fields (GF) under hard decisions. The major drawback is low fault tolerance. When soft information about the channel output is available, the decoding performance is improved about 2~3 dB in soft decision situations [

The paper is organized as follows. Section

According to the algebraic properties of BCH codes, if no error occurs in transmission, all syndromes equal zeros. The syndromes are calculated as follows [

In (

In [

It is difficult to apply (

We let

Using (

According to [

According to the coding theories [

The purpose of blind recognition is to estimate the code length and parity check matrix

In a cognitive radio system, though the transmitters choose optimized code length and code rate, we can limit the range of them to simplify the reconstruction complexity of the encoder parameters for cognitive receivers. We can limit the fact that transmitters send primitive BCH coded packets in regular code length of

Before the code rate is confirmed, the number of rows of the parity check matrix

For each code length

In (

When the code length is confirmed, the number of rows in the parity check matrix

The number of rows in

A simple solution is modifying (

For the convenience of computer recognition, we propose the judgment of the code rate in the computer program by computing the criteria function as follows:

The error-correcting capacity

Finally, the parity check matrix

Computer simulation results of the proposed algorithm are shown in this section. In the simulations, we assume that the transmitter is sending a binary sequence of codewords and using a Binary Phase Shift Keying (BPSK) modulation. The propagation channel is corrupted by an Additive White Gaussian Noise (AWGN) with the variance

Special property of the root

In the simulations, we choose statistical samples including 50 blocks. The curves show that our proposed algorithm yields a better performance. The curves of PFR of our proposed algorithm fall rapidly when SNR increases and the PFR is much lower than that of the RIDERS algorithm. Note that the RIDERS algorithm could not estimate the code length for the BCH (127, 71) codes; even SNR is high. The authors of [

We also compare the calculation complexity of the proposed algorithm and the RIDERS algorithm in [

Comparing of elapsed time between proposed and RIDERS algorithms.

After estimating of the code length

LLRs on different code roots of the BCH (63, 51) codes.

Then the code parameters are completely confirmed. The stems of

Criteria function

Probabilities of fault recognition of parity check matrix on different SNRs.

A new blind recognition of BCH codes for cognitive radios in soft decision situation is presented. The code length is estimated firstly by checking the LLRs of the minimum parity check matrix and the code rate and whole check matrix are reconstructed by searching code roots. Simulations show that our proposed blind recognition algorithm yields better performance than one of the previous ones.

The authors declare that there is no conflict of interests regarding the publication of this paper.