On the distribution of computation for sequential decoding using the stack algorithm

An analytical procedure is presented for generating the computational distribution for the Zigangirov-Jelinek stack algorithm. Multitype branching processes are employed to develop a procedure for estimating sequential decoding computation, without the need for simulation, but with sufficient accuracy to be a valid design tool. At information rates about the cutoff rateR_{o}the calculated computational performance is virtually Identical to that obtained by time consuming simulations

On the error probability of general trellis codes with applications to sequential decoding

An upper bound on the average error probability for maximum-likelihood decoding of the ensemble of randomL-branch binary trellis codes of rateR = 1/nis given which separates the effects of the tail lengthTand the memory lengthMof the code. It is shown that the bound is independent of the lengthLof the information Sequence whenM geq T + [nE_{VU}(R)]^{-1} log_{2} L. The implication that the actual error probability behaves similarly is investigated by computer simulations of sequential decoding utilizing the stack algorithm. These simulations confirm the implication which can thus be taken as a design rule for choosingMso that the error probability is reduced to its minimum value for a givenT

Some long rate one-half binary convolutional codes with an optimum distance profile

This correspondence gives a tabulation of long systematic, and long quick-look-in (QLI) nonsystematic, rateR = 1/2binary convolutional codes with an optimum distance profile (ODP). These codes appear attractive for use with sequential decoders

Further results on binary convolutional codes with an optimum distance profile

Fixed binary convolutional codes are considered which are simultaneously optimal or near-optimal according to three criteria: namely, distance profiled, free distanced_{ infty}, and minimum number of weightd_{infty}paths. It is shown how the optimum distance profile criterion can be used to limit the search for codes with a large value ofd_{infty}. We present extensive lists of such robustly optimal codes containing rateR = l/2nonsystematic codes, several withd_{infty}superior to that of any previously known code of the same rate and memory; rateR = 2/3systematic codes; and rateR = 2/3nonsystematic codes. As a counterpart to quick-look-in (QLI) codes which are not "transparent," we introduce rateR = 1/2easy-look-in-transparent (ELIT) codes with a feedforward inverse(1 + D,D). In general, ELIT codes haved_{infty}superior to that of QLI codes

A fast algorithm for computing distance spectrum of convolutional codes

New rate-compatible convolutional (RCC) codes with high constraint lengths and a wide range of code rates are presented. These new codes originate from rate 1/4 optimum distance spectrum (ODS) convolutional parent encoders with constraint lengths 7-10. Low rate encoders (rates 115 down to 1/10) are found by a nested search, and high rate encoders (rates above 1/4) are found by rate-compatible puncturing. The new codes form rate-compatible code families more powerful and flexible than those previously presented. It is shown that these codes are almost as good as the existing optimum convolutional codes of the same fates. The effects of varying the design parameters of the rate-compatible punctured convolutional (RCPC) codes, i.e., the parent encoder rate, the puncturing period, and the constraint length, are also examined. The new codes are then applied to a multicode direct-sequence code-division multiple-access (DS-CDMA) system and are shown to provide good performance and rate-matching capabilities. The results, which are evaluated in terms of the efficiency for Gaussian and Rayleigh fading channels, show that the system efficiency increases with decreasing code rat

A generalization of the predictable degree property to rational convolutional encoding matrices

The predictable degree property was introduced by Forney (1970) for polynomial convolutional encoding matrices. In this paper two generalizations to rational convolutional encoding matrices are discusse

Woven Graph Codes: Asymptotic Performances and Examples

Constructions of woven graph codes based on constituent block and convolutional codes are studied. It is shown that within the random ensemble of such codes based on $s$-partite, $s$-uniform hypergraphs, where $s$ depends only on the code rate, there exist codes satisfying the Varshamov-Gilbert (VG) and the Costello lower bound on the minimum distance and the free distance, respectively. A connection between regular bipartite graphs and tailbiting codes is shown. Some examples of woven graph codes are presented. Among them an example of a rate $R_{\rm wg}=1/3$ woven graph code with $d_{\rm free}=32$ based on Heawood's bipartite graph and containing $n=7$ constituent rate $R^{c}=2/3$ convolutional codes with overall constraint lengths $\nu^{c}=5$ is given. An encoding procedure for woven graph codes with complexity proportional to the number of constituent codes and their overall constraint length $\nu^{c}$ is presented.Comment: Submitted to IEEE Trans. Inform. Theor

Chained Gallager codes

The ensemble of regular Low-Density Parity-Check (LDPC) codes introduced by Gallager is considered. Using probabilistic arguments a lower bound on the normalized minimum distance is derived. A new code construction, called Chained Gallager codes, is introduced as the combination of two Gallager codes and its error correcting capabilities are studied