Blind identification of code word length for non-binary error-correcting codes in noisy transmission

Zrelli et al. EURASIP Journal on Wireless Communications and Networking Blind identification of code word length for non-binary error-correcting codes in noisy transmission 0 Universite de Brest; CNRS, UMR 6285 Lab-STICC , 6 avenue Victor Le Gorgeu, 29238 Brest , France 1 Universite Europeenne de Bretagne , 5 Boulevard Laennec, 35000 Rennes , France In cognitive radio context, the parameters of coding schemes are unknown at the receiver. The design of an intelligent receiver is then essential to blindly identify these parameters from the received data. The blind identification of code word length has already been extensively studied in the case of binary error-correcting codes. Here, we are interested in non-binary codes where a noisy transmission environment is considered. To deal with the blind identification problem of code word length, we propose a technique based on the Gauss-Jordan elimination in GF(q) (Galois field), with q = 2m, where m is the number of bits per symbol. This proposed technique is based on the information provided by the arithmetic mean of the number of zeros in each column of these matrices. The robustness of our technique is studied for different code parameters and over different Galois fields. Cognitive radio; Blind identification; Non-binary error-correcting codes; Galois field - Error-correcting codes are frequently used in modern digital transmission systems in order to improve the communication quality. These codes are designed to achieve a good immunity against channel impairments by introducing redundancy in the informative data. Due to the complexity of both encoding and especially decoding procedures, the majority of research and practical implementations of real-time embedded systems were often restricted to encoders manipulating binary data, i.e., elements of the Galois field GF(2). Over the last decade, low-density parity check (LDPC) codes and turbo codes over GF(2) have attracted considerable interest of many researchers due to their excellent error correction capability. They have been generalized to finite fields GF(q) [1,2], where q = 2m, and are among the most widely used errorcorrecting codes in wireless communication standards. It has been shown in [1] that non-binary LDPC codes perform generally better than binary LDPC codes and turbo codes. However, the major drawback of these codes is their decoding complexity for a large Galois field order q [3,4]. Low complexity decoding algorithms have recently been proposed [5,6], thus allowing the use of non-binary LDPC codes in practical implementations. Our main research interests are focused on non-binary error-correcting codes in order to blindly identify their parameters. This topic is a part of a non-cooperative context like a military interception or cognitive radio applications. In this case, the receiver has no knowledge about the parameters used to encode the information at the transmitter. The solution is to design an intelligent receiver which is able to blindly identify the encoder parameters from the only knowledge of the received data stream. This blind identification function of the receiver permits to increase the data rate transmission, since it will be unnecessary to transmit supplementary information about the encoder parameters with the useful data. Such intelligent receiver is able to adapt automatically itself to the development of new high-performance coding schemes and the fast evolution of new communication standards without equipment change. In this work, we are only interested in blindly identifying the code word length of linear nonbinary block codes. In the case of the interception, this parameter can not be transmitted. Likewise, if we want to change the encoder or get out of the list of possible choice of encoders, the code word length is not transmitted. In this context, the published research results have been restricted so far to the blind recognition of the code word length of binary codes. To the best of our knowledge, this paper introduces, for the first time, an approach to blindly identify the code word length of non-binary codes in noisy conditions. In this work, the aim is to blindly identify the code word length from the only knowledge of received data. The authors in [7] proposed a technique of identification of non-binary LDPC parameters, but the identification is not blind because it is based on using a predefined candidate set of encoders which is known by both the transmitter and the receiver. Furthermore, this technique only works with LDPC codes unlike our proposed technique, which is general and suitable for all block codes. In our paper, the proposed blind identification technique is based on a generalization of an existing method used for binary codes. The principle of this generalization will be explained in this paper without specifying in details its detection performances. So, we present here state-of-the-art techniques to identify the code word length of binary linear block codes. The idea of these techniques is to find a basis of a dual code composed of parity check relations. For this purpose, an approach based on finding code words of small Hamming weight [8,9] was improved by Valembois [10] by using statistical hypothesis tests and recently by Cluzeau [11,12] and Cte [13]. A second approach based on linear algebra theory was introduced in [14] for noiseless channel. This approach permits to recover the length of code words by studying behaviors of the rank of matrices composed of received bits. However, the rank criterion was exploited without providing an algebraic and theoretical justification of such behavior. In [15], the use of this criterion was justified. In [16], the rank criterion approach was generalized to convolutional codes over GF(q), where q > 2, assuming a noiseless transmission, but it was shown that this generalized technique can be also performed to non-binary linear block codes. In noisy transmissions, a technique based on the Gauss elimination in GF(2) was applied in [17-19] to matrices composed of noisy received bits in order to find the number of almost dependent columns permitting the identification of the code word length in the case of binary error-correcting codes. Indeed, an almost dependent column of a matrix composed of noisy received symbols corresponds to a column which may be a linear combination of some preceding columns without the presence of erroneous symbols and which leads to a column that contains more zero elements after the Gauss elimination. Compared to previous works, we demonstrate here that it is possible to generalize the blind identification technique proposed in [17,18] to non-binary block codes provided that the Galois field parameters (the cardinality and the primitive polynomial) are known by the receiver. To identify the primitive polynomial, an algorithm of identification was proposed in [20]. To achieve our purpose, it is necessary to identify the number o (...truncated)