Asymptotic distance and convergence analysis of braided protograph convolutional codes

We show that the generator polynomials of certain cyclic codes define noncatastrophic fixed convolutional codes whose free distances are lowerbounded by the minimum distances of the cyclic codes. This result is used to construct convolutioual codes with free distance equal to the constraint length and to derive convolutional codes with good free distances from the BCH codes. Finally, a class of time-varying codes is constructed for which the free distance increases linearly with the constraint length.

We study a serially interleaved concatenated code construction, where the outer code is a standard convolutional code, and the inner code is a recursive convolutional code of rate 1. We focus on the ubiquitous inner differential encoder (used, in particular, to resolve phase ambiguities), double differential encoder (used to resolve both phase and frequency ambiguities), and another rate 1 recursive convolutional code of memory 2. We substantiate analytically the rather surprising result, that the error probabilities corresponding to a maximum-likelihood (ML) coherently detected antipodal modulation over the additive white Gaussian noise (AWGN) channel for this construction are advantageous as compared to the stand-alone outer convolutional code. This is in spite of the fact that the inner code is of rate 1. The analysis is based on the tangential sphere upper bound of an ML decoder, incorporating the ensemble weight distribution (WD) of the concatenated code, where the ensemble is generated by all random and uniform interleavers. This surprising result is attributed to the WD thinning observed for the concatenated scheme which shapes the WD of the outer convolutional code to resemble more closely the binomial distribution (typical of a fully random code of the same length and rate). This gain is maintained regardless of a rather dramatic decrease, as demonstrated here, in the minimum distance of the concatenated scheme as compared to the minimum distance of the outer stand-alone convolutional code. The advantage of the examined serially interleaved concatenated code, given in terms of bit and/or block error probability which is decoded by a practical suboptimal decoder, over the optimally decoded standard convolutional code is demonstrated by simulations, and some insights into the performance of the iterative decoding algorithm are also discussed. Though we have investigated only specific constructions of constituent inner (rate 1) and outer codes, we trust, hinging on the rational of the arguments here, that these results extend to many other constituent convolutional outer codes and rate 1 inner recursive convolutional codes.

We propose an efficient Adaptive Random Convolutional Network Coding (ARCNC)\nalgorithm to address the issue of field size in random network coding. ARCNC\noperates as a convolutional code, with the coefficients of local encoding\nkernels chosen randomly over a small finite field. The lengths of local\nencoding kernels increase with time until the global encoding kernel matrices\nat related sink nodes all have full rank. Instead of estimating the necessary\nfield size a priori, ARCNC operates in a small finite field. It adapts to\nunknown network topologies without prior knowledge, by locally incrementing the\ndimensionality of the convolutional code. Because convolutional codes of\ndifferent constraint lengths can coexist in different portions of the network,\nreductions in decoding delay and memory overheads can be achieved with ARCNC.\nWe show through analysis that this method performs no worse than random linear\nnetwork codes in general networks, and can provide significant gains in terms\nof average decoding delay in combination networks.\n

In this paper we present a study of Bit Error Rate (BER), for Digital Audio Broadcasting (DAB) system, employing Coded OFDM with different channel coding schemes. Analysis is carried out for convolutional coded and turbo coded data in an Additive White Gaussian Channel (AWGN) based on different constraint lengths and code generator polynomials used for coding. A comparative study on the computational complexity is also done by applying an audio signal and measuring the data processing time per frame, on computers with different processor speeds. It is shown that a coding gain of approximately 6 dB is achieved using turbo coding when compared to convolutional coding, at a cost of higher computational complexity.

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.

The minimum free distance (MFD) of convolutional error-correcting codes is a powerful and well-known parameter for indicating the behaviour of the communication system via an AWGN channel with medium and high SNR. But in many cases it happens that the MFD theory fails. The letter provides some examples where codes with a high MFD are being defeated by codes with lower MFD. Then a new method called the effective minimum free distance is introduced to achieve greater simplicity and to strengthen the MFD theory. Software simulation for some codes with constraint lengths 3 and 4 demonstrate this idea. The Viterbi decoding algorithm is used for the simulation program. The truncated generator function of a code is modified into a new, effective terms form that presents a very practical measure on the error correctability of the code.

This paper presents new bounds to be used in the search for the free distance (D/sub free/) of infinite response codes based on filtering a PAM modulated signal. The bounds extend the two main criteria used to prune paths with trellis codes, namely: path weight comparisons: from each state only the path with the smallest weight is extended; and bounding: if the weight is larger than an upper bound on D/sub free/ then no path is extended. If a PAM signal is filtered with an IIR filter, then we have a linear tree code, and the paths do not merge. In addition, the weight D/sub free/ is reached only in the limit. We show that, by using more powerful bounds, it is possible to compare paths in the cases of "near merges," and to find when a path corresponds to D/sub free/ in early stages of the search. The new bounds are useful for several types of convolutional coding, and for that reason we present a quite general approach, and exemplify the solutions for filtered PAM and also for binary convolutional codes (BCC).< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

The result of a search for the world's second type II (doubly-even and self-dual) convolutional code is reported. A rate R=4/8, 16-state, time-invariant, convolutional code with free distance dfree=8 was found to be type II. The initial part of its weight spectrum is better than that of the Golay convolutional code (GCC). Generator matrices and path weight enumerators for some other type II convolutional codes are given. By the “wrap-around” technique tail-biting versions of (32, 18, 8) Type II block codes are constructed

Let H(D) be the parity-check matrix of an LDPC convolutional code corresponding to the parity-check matrix H of a QC code obtained using the method of Tanner et al. We see that the entries in H(D) are all monomials and several rows (columns) have monomial factors. Let us cyclically shift the rows of H. Then the parity-check matrix H'(D) corresponding to the modified matrix H' defines another convolutional code. However, its free distance is lower-bounded by the minimum distance of the original QC code. Also, each row (column) of H'(D) has a factor different from the one in H(D). We show that the statespace complexity of the error-trellis associated with H'(D) can be significantly reduced by controlling the row shifts applied to H with the error-correction capability being preserved.

A trellis code encoded by using the encoder of a convolutional code C with a short constraint length followed by an additional processing unit is equivalent to a trellis code with a large constraint-length. In 1993, Hellstern proposed a trellis coding scheme for which the processing unit consists of a delay processor and a signal mapper. With Hellstern's scheme, trellis codes with large free distances can be constructed. In this paper, we propose two trellis coding schemes. For the first scheme, the processing unit is composed of multiple pairs of delay processors and signal mappers. For the second scheme, the processing unit is composed of a convolutional processor and a signal mapper, where a convolutional processor is a rate 1 convolutional code. The trellis code constructed from each of the proposed schemes can be suboptimally decoded by using the trellis of the convolutional code C with some feedback information. Either of the proposed schemes can produce a trellis code that has a larger bound on free distance and better error performance as compared to the trellis code constructed from Hellstern's scheme based on the same convolutional code C.

Woven convolutional codes with one tailbiting component code are studied and their generator matrices are given. It is shown that, if the constituent encoders are identical, a woven convolutional encoder with an outer convolutional warp and one inner tailbiting encoder (WIT) generates the same code as a woven convolutional encoder with one outer tailbiting encoder and an inner convolutional warp (WOT). However, for rate Rtb < 1 tailbiting encoders, the WOT cannot be an encoder realization with a minimum number of delay elements. Lower bounds on the free distance and active distances of woven convolutional codes with a tailbiting component code are given. These bounds are equal to those for woven codes consisting exclusively of unterminated convolutional codes. However, for woven convolutional codes with one tailbiting component code, the conditions for the bounds to hold are less strict.

In this paper, we concern with designing and implementing a convolutional encoder and Viterbi decoder which are the essential block in digital communication systems using FPGA technology. Convolutional coding is a coding scheme used in communication systems including deep space communications and wireless communications. It provides an alternative approach to block codes for transmission over a noisy channel. The block codes can be applied only for the block of data. The convolutional coding has an advantage over the block codes in that it can be applied to a continuous data stream as well as to blocks of data.The motivation of this paper is to realize a Viterbi decoder having Constraint length 9 and code rate 1/2 by Xilinx 12.4i tools.

Throughput is one of the most important factors in wireless communication. This paper studies the throughput efficiency of Bluetooth network using Enhanced Data Rate (EDR) packets. This paper, proposes improving the throughput efficiency of JPEG image transmission over mobile Bluetooth network using Enhanced Data Rate (EDR) packets. This paper uses the 2DH 3 and proposed 2DM 3 EDR Asynchronous Connectionless (ACL) packets. This paper presents a proposed using efficient error control schemes to improve the throughput of Bluetooth systems. A comparison study between different propositions is held in the paper to choose an efficient case over mobile Bluetooth network. The simulation experiments are carried over correlated Rayleigh fading channel. Our experiments reveal that the proposed convolutional code with constraint length K=3 and 7 improves the throughput efficiency of JPEG image at low SNR values. In our simulation results show that the convolutional codes are good over correlated fading channel more than the traditional Bluetooth error correction scheme for EDR Bluetooth packets. At higher SNR values (SNR>28dB) the standard uncoded 2DH3 packets gives a good throughput. Finally, using convolutional code with different K values improves the throughput over mobile Bluetooth network.

The performance of coded multi-pulse pulse position modulation (MPPM) consisting of m slots and 2 pulses, denoted as (m, 2) MPPM, with imperfect slot synchronization is analyzed. Convolutional codes and Reed-Solomon (RS) codes are employed for (m, 2) MPPM, and the bit error probability of coded (m, 2) MPPM in the presence of the timing offset is derived. In each coded (m, 2) MPPM, we compare the performance of some different code rate systems. Moreover, we compare the performance of both systems at the same information bit rate. It is shown that in both coded systems, the performance of code rate-1/2 coded MPPM is the best when the timing offset is small. Further, convolutional coded (m, 2) MPPM on the constraint length k/spl ges/7 performs better than Reed-Solomon coded (m, 2) MPPM for the same code rate. >

In this paper, we propose a new type of code called Trellis-based Quasi-Cyclic (TQC)-LDPC convolutional code, which is a special case of protograph-based LDPC convolutional codes. The proposed TQC-LDPC convolutional code can be derived from any QC-LDPC block code by introducing trellis-based convolutional dependency to the code. The main advantage of the proposed TQC-LDPC convolutional code is that it allows reduced decoder complexity and input granularity (which is defined as the minimum number of input information bits the code requires to generate a codeword) while maintaining the same bit error-rate as the underlying QC-LDPC block code ensemble. We also propose two related power-efficient encoding methods to increase the code rate of the derived TQC-LDPC convolutional code. The newly derived short constraint length TQC-LDPC convolutional codes enable low complexity trellis-based decoders and one such decoder is proposed and described in this paper (namely, QC-Viterbi). The TQC-LDPC convolutional codes and the QC-Viterbi decoder are compared to conventional LDPC codes and Belief Propagation (BP) iterative decoders with respect to bit-error-rate (BER), signal-to-noise ratio (SNR), and decoder complexity. We show both numerically and through hardware implementation results that the proposed QC-Viterbi decoder outperforms the BP iterative decoders by at least 1 dB for same complexity and BER. Alternatively, the proposed QC-Viterbi decoder has 3 times lower complexity than the BP iterative decoder for the same SNR and BER. This low decoding complexity, low BER, and fine granularity makes it feasible for the proposed TQC-LDPC convolutional codes and associated trellis-based decoders to be efficiently implemented in high data rate, next generation mobile systems.