Channel coding in spread spectrum systems

sufficient length are good from this angle. And yet finding specific code rules allowing Shannon’s limit to be approached remained impenetrable up to the moment of discovering turbo codes in 1993, although lots of important and widely utilized results had been obtained in pursuing this target.

Of course, modern coding theory is too sophisticated to permit pressing even its initial basics into a brief chapter. It looks all the more inappropriate against the background of the key role of coding theory in general information technology, of which spread spectrum communications is only a particular branch. Still, the importance of channel coding in spread spectrum systems is extremely high, since the majority of them are designed to operate in a very noisy environment and, what is more, many themselves create strong intra-system interference (MAI in asynchronous CDMA). The MAI effects, unlike the natural (thermal) noise, cannot be overcome just by brute force, i.e. increasing signal power, since all users have equal rights and gain in SIR for one of them obtained in this way turns into a loss for the others (see Sections 4.5 and 4.6). This leaves the designer with only two resources for withstanding MAI: increasing the spreading factor and involving powerful channel codes. Trying to handle the available space reasonably, we limit this chapter to only coding issues related to the commercial 2G and 3G spread spectrum standards cdmaOne, UMTS and cdma2000. Accordingly, the mathematical tools, designations and description manner below are narrowly adapted to match this particular task in the most economical and fast way. We refer readers interested in a more universal scope to the books on coding theory (e.g. [31,33,91]).

Let us start with some basic classification of channel codes. The first feature to distinguish between them is alphabet size, according to which we talk about binary, ternary etc. codes. Although the range of applications of non-binary (e.g. Reed–Solomon or Ungerboeck) codes is pretty wide nowadays, we concentrate on only binary ones, which are used in the specifications mentioned above. Another form of classification is the way in which information data are mapped onto the codewords or code vectors (i.e. sequences of code symbols carrying the transmitted message). The point is that any channel coding consists of inserting some redundancy into the message, making the transmitted signals more distant from each other, and thereby reducing the risk of confusion between them. Depending on the way of adding this redundancy, all channel codes are classified into block or tree (trellis) codes. A characteristic of block codes is segmentation of the source bitstream, which is divided into blocks of k information bits, every block being encoded into n > k binary symbols. In so doing, the redundant n k symbols serve to protect only the k source bits of their own codeword. Codewords of tree (e.g. convolutional) codes have a different structure: a continuous-source bitstream is encoded into an infinite stream of code symbols (codestream) with no fragmentation (see details in Section 9.3).

When it arrives at the receiving end the encoded word should be mapped back onto the transmitted data bits. This operation is called decoding. Physically, due to modulation, any codeword travels via the channel as some signal. When transmitted over the AWGN (or another state-continuous) channel, the signal gets corrupted by noise whose instantaneous samples are continuous. The optimal (ML) decision strategy of a receiver in the case of Gaussian noise is equivalent to the minimum Euclidean distance rule (see Section 2.1), which means declaring true the signal closest to the observation obtained. This straightforward procedure ends directly in decoded data bits and bears the name (along with its numerous approximations) soft decoding. The complexity of