There are many good periodically time-varying convolutional codes

It is shown empirically that the number of good periodically time-varying convolutional codes increases exponentially with the period for any set of parameters. Hence, they can be used to enhance the security of cryptosystems without sacrificing error correction capability. It is shown that some periodically time-varying convolutional codes improve the free distance compared with fixed codes     

Is the class of cyclic codes asymptotically good?

There is the long-standing question whether the class of cyclic codes is asymptotically good. By an old result of Lin and Weldon, long Bose-Chaudhuri-Hocquenhem (BCH) codes are asymptotically bad. Berman proved that cyclic codes are asymptotically bad if only finitely many primes are involved in the lengths of the codes. We investigate further classes of cyclic codes which also turn out to be asymptotically bad. Based on reduction arguments we give some evidence that there are asymptotically good sequences of binary cyclic codes in which all lengths are prime numbers provided there is any asymptotically good sequence of binary cyclic codes.     

Structure and constructions of cyclic convolutional codes

The encoded sequences of an(n,k)convolutional code are treated as sequences of polynomials in the ring of polynomials moduloX^{n} - 1. Any such sequence can then be written as a power series in two variablesw(X,D), where the polynomial coefficient ofD^{j}is the "word" at time unitjin the sequence. Necessary and sufficient conditions on the ring "multiplication" for the set of such sequences so that the set becomes alinear associative algebra are derived. Cyclic convolutional codes (CCC's)are then defined to be left ideals in this algebra. A canonical decomposition of a CCC into minimal ideals is given which illuminates the cyclic structure. As an application of the ideas in the paper, a number of CCC's with large free distance are constructed.     

New short constraint length convolutional code constructions for selected rational rates (Corresp.)

New short constraint length convolutional code constructions are tabulated for ratesR=(n-k)/n, k=1,2, cdots ,n-1withn=2, 3,cdots ,8, and for constraint lengthsK=3,4, cdots,8. These codes have been determined by iterative search based upon a criterion of optimizing the free distance profile. Specifically, these codes maximize the free distanced_{f}while minimizing the number of adversaries in the distance, or weight, spectrum. In several instances we demonstrate the superiority of these codes over previously published code constructions at the same rate and constraint length. These codes are expected to have a number of applications, including combined source-channel coding schemes as well as coding for burst or impulsive noise channels.     

On asymptotically optimum rate 1/n convolutional codes for a givenconstraint length

The criterion used to find good convolutional codes has traditionally been the maximization of the free distance for a given constraint length and code rate. In this letter we approach convolutional code design from a different perspective. We assume no constraints in the rate of the code, and the only restriction is in the constraint length. That is, we assume we can utilize as much bandwidth as necessary but we are complexity-limited by the constraint length we can afford. The results are optimum codes for a given constraint length, which can find application, for example, in CDMA systems     

A class of DC-free subcodes of convolutional codes

We describe a class of DC-free subcodes of convolutional codes that satisfy certain runlength constraints and that also possess error-correcting capability. The running disparity and the maximum runlength of these codes are bounded by quantities that are independent of the free distance. They can be decoded using a Viterbi decoder for the underlying convolutional code     

A search for good convolutional codes to be used in theconstruction of turbo codes

Recursive systematic convolutional encoders have been shown to play a crucial role in the design of turbo codes. We recall some properties of binary convolutional encoders and apply them to a search for good constituent convolutional codes of turbo codes. Tables of the “best” recursive systematic convolutional encoders found are presented for various rates, together with the average bit-error probability performances of some turbo codes using them     

Partitioning of convolutional codes using a convolutional scrambler

Recently a partitioning method for convolutional codes of rate 1/N has been proposed. The authors investigate an improved partitioning scheme, which is illustrated by a code with small constraint length. This new method leads to better free distances in the partitioned subcodes     

A note on asymptotically catastrophic convolutional codes of rate(n-1)/n

Convolutional codes with rate R=(n-1)/n,n⩾2, are defined in terms of their minimal parity check matrices. The matrices are represented by a binary vector notation introduced by Ytrehus (1992). The upper bounds on ω0 (minimum average weight per branch) are presented. Many classes of rate (n-1)/n convolutional codes are shown to be asymptotically catastrophic     

An extensive search for good punctured rate-k/(k+1) recursive convolutional codes for serially concatenated convolutional codes

In many practical applications requiring variable-rate coding and/or high-rate coding for spectral efficiency, there is a need to employ high-rate convolutional codes (CC), either by themselves or in a parallel or serially concatenated scheme. For such applications, in order to keep the trellis complexity of the code constant and to permit the use of a simplified decoder that can accommodate multiple rates, a mother CC is punctured to obtain codes with a variety of rates. This correspondence presents the results of extensive search for optimal puncturing patterns for recursive convolutional codes leading to codes of rate k/(k+1) (k an integer) to be used in serially concatenated convolutional codes (SCCC). The code optimization is in the sense of minimizing the required signal-to-noise ratio (SNR) for two target bit-error rate (BER) and two target frame-error rate (FER) values. We provide extensive sample simulation results for rate-k/(k+1) SCCC codes employing our optimized punctured CC.     

New very high rate punctured convolutional codes

New very high rate punctured convolutional codes suitable for Viterbi decoding are presented. These codes extend recent results on high rate convolutional codes by employing an efficient computer search technique and are optimum in that they minimise the residual bit error rate over all puncturing patterns given a particular basis code. Tables of new codes of rate (n-1)/n are given for n=9, 10, 11 and 12     

High rate convolutional codes with good distance profiles (Corresp.)

The result of a computer search for systematic convolutional codes with rates(N - 1)/NforNfrom 3 to 8 is presented. The codes have rapidly growing column distance, making them attractive for sequential decoding.     

New rate-compatible punctured convolutional codes for Viterbidecoding

New good rate-P/(P+δ) rate-compatible punctured convolutional (RCPC) codes for 2⩽P⩽7 and 1⩽δ⩽(n-1)P were found and tabulated, These codes have been determined by iterative search based upon a criterion of maximizing the free distance and were generated by periodically puncturing their rate-1/n mother codes of memory 2⩽M⩽6 and n=2. These codes are expected to find their applications in unequal error protection schemes employing Viterbi decoding     

A class of linear codes with good parameters

A construction of linear codes with good parameters is given. Based on Brouwer's table, more than 100 new codes are obtained from our construction     

New class of time-varying filters

A new class of time-varying lowpass and highpass filters is described in which the stopband attenuation is obtained by outphasing in a quadrature-modulation arrangement, the undesired associated frequency translation or inversion being cancelled by a suitably chosen second step of quadrature demodulation or both; bandpass and bandstop filters can be obtained as combinations of lowpass and highpass filters.     

On error exponents for woven convolutional codes with one tailbiting component code

An error exponent for woven convolutional codes (WCC) with one tailbiting component code is derived. This error exponent is compared with that of the original WCC. It is shown that for WCC with outer warp, a better error exponent is obtained if the inner code is terminated with the tailbiting method. Furthermore, it is shown that the decoding error probability decreases exponentially with the square of the memory of the constituent convolutional encoders, while the decoding complexity grows exponentially only with the memory.     

Some periodic convolutional codes better than any fixed code (Corresp.)

Some(n_{o}=2; k_{o}=1)noncatastrophic periodic convolutional codes with memoryM=4are given that have the same free distance,d_{infty}, as the best fixed code but have both a smaller number of paths of weightd_{infty}per time instant and a smaller average number of information bit errors per such path for periodsT=2, 3, 4, and5. It is also shown that an(n_{0}, k_{0})code of periodTis equivalent to a fixed code with parameters(Tn_{0}, Tk_{0}).     

Design and performance analysis of a new class of rate compatible serially concatenated convolutional codes

In this paper, a novel class of serially concatenated convolutional codes (SCCCs) is addressed. In contrast to standard SCCCs, where high rates are obtained by puncturing the outer code, the heavy puncturing is moved to the inner code, which can be punctured beyond the unitary rate. We derive analytical upper bounds on the error probability of this code structure by considering an equivalent code construction consisting of the parallel concatenation of two codes, and address suitable design guidelines for code optimization. It is shown that the optimal puncturing of the inner code depends on the outer code, i.e., it is interleaver dependent. This dependence cannot be tracked by the analysis for standard SCCCs, which fails in predicting code performance. Based on the considerations arising from the bounds analysis, we construct a family of rate-compatible SCCCs with a high level of flexibility and a good performance over a wide range of code rates, using simple constituent codes. The error rate performance of the proposed codes is found to be better than that of standard SCCCs, especially for high rates, and comparable to the performance of more complex turbo codes.     

Serial concatenation of a block code and a 2D convolutional code

Multidimensional Systems and Signal Processing - In this paper we study two different concatenation schemes of twodimensional (2D) convolutional codes. We consider Fornasini–Marchesini state...