The trellis complexity of convolutional codes
نویسندگان
چکیده
It has long been known that convolutional codes have a natural, regular trellis structure that facilitates the implementation of Viterbi's algorithm [30,10]. It has gradually become apparent that linear block codes also/]ave a natural, though not in general a regular, "minimal" trellis structure, which allows them to be decoded with a Viterbi-1ike algorithn] [2,31,22,11,27,14,12,16,24,25,8,15]. In both cases, the complexity of tile Viterbi decoding algorithm can be accurately estimated by the number of trellis edges per encoded bit. It would, therefore, appear that we are in a good position to make a fair comparison of the Viterbi decoding complexity of block and convolutional codes. Unfortunately, however, this comparison is somewhat muddled by the fact that some convolutional codes, tile punctured convolutional codes [4], are known to have trellis representations that are sig_Jificantly less complex than the conventional trellis. In other words, ttle conventional trel]is representation for a convolutional code may not be the minimal trellis representation. Thus, ironically, at present we seem to know more about the minimal trel]is representation for block than for convolutional codes. In this article, we provide a remedy, by developing a theory of minimal trellises for convolutional codes. (A similar theory has recently been given by Sidorenko and Zyabloy [29].) This allows us to make a direct performal_ce-complexity comparison for block and convolutional codes. A by-product of our work is an algorithm for choosing, from among a11 generator matrices for a given convolutional code, what we call a trellis-minimal generator matrix, from which the minimal trellis for the code can be directly constructed. Another by-product is that, in the new theory, punctured convolutional codes no longer appear as a special class, but simply as high-rate convolutional codes whose trellis complexity is unexpectedly small.
منابع مشابه
Trellis-Coded Quantization Based on Maximum-Hamming-Distance Binary Codes
Most design approaches for trellis-coded quantization take advantage of the duality of trellis-coded quantization with trellis-coded modulation, and use the same empiricallyfound convolutional codes to label the trellis branches. This letter presents an alternative approach that instead takes advantage of maximum-Hamming-distance convolutional codes. The proposed source codes are shown to be co...
متن کاملChannel Coding Techniques with Emphasis on Convolutional and Turbo Codes
In this thesis, a family of low complexity convolutional codes is constructed, by modifying appropriately the trellis diagram of punctured convolutional codes. The goal is to improve performance at the expense of a reasonable low increase of the trellis complexity. Many new convolutional codes of various code rates and values of complexity are provided. In many cases, a small increase in comple...
متن کاملOn the Intractability of Permuting a Block Code to Minimize Trellis Complexity [Correspondence] - Information Theory, IEEE Transactions on
A novel trellis design technique for both block and convolutional codes based on the Shannon product of component block codes is introduced. Using the proposed technique, structured trellises for block and convolutional codes have been designed. It is shown that the designed trellises are minimal and allow reduced complexity Viterbi decoding. Zndex Terms-Linear codes, trellis structure, product...
متن کاملP2 Codes: Pragmatic Trellis Codes Utilizing Punctured Convolutional Codes
In a paper [ I ] , a pragmatic approach to the design of trellis codes was described whereby the basic engine of the trellis decoder was a Viterbi Decoder for the de facto industry and government standard, rate 1/2, 64state, convolutional code. In that paper, codes for 8PSK and 16-PSK modulation were described which performed almost as well as the best trellis codes of comparable complexity (fo...
متن کاملMinimal Code(Error)-Trellis Module Construction for Rate-k/n Convolutional Codes: Extension of Yamada-Harashima-Miyakawa's Construction
Yamada, Harashima, and Miyakawa proposed to use a trellis constructed based on a syndrome former for the purpose of Viterbi decoding of rate-(n − 1)/n convolutional codes. In this paper, we extend their code-trellis construction to general rate-k/n convolutional codes. We show that the extended construction is equivalent to the one proposed by Sidorenko and Zyablov. Moreover, we show that the p...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- IEEE Trans. Information Theory
دوره 42 شماره
صفحات -
تاریخ انتشار 1996