Showing papers on "Sequential decoding published in 1993"
23 May 1993
TL;DR: In this article, a new class of convolutional codes called turbo-codes, whose performances in terms of bit error rate (BER) are close to the Shannon limit, is discussed.
Abstract: A new class of convolutional codes called turbo-codes, whose performances in terms of bit error rate (BER) are close to the Shannon limit, is discussed. The turbo-code encoder is built using a parallel concatenation of two recursive systematic convolutional codes, and the associated decoder, using a feedback decoding rule, is implemented as P pipelined identical elementary decoders. >
5,963 citations
TL;DR: This decoding procedure is a generalization of Peterson's decoding procedure for the BCH codes and can be used to correct any ((d*-1)/2) or fewer errors with complexity O(n/sup 3/), where d* is the designed minimum distance of the algebraic-geometric code and n is the codelength.
Abstract: A simple decoding procedure for algebraic-geometric codes C/sub Omega /(D,G) is presented. This decoding procedure is a generalization of Peterson's decoding procedure for the BCH codes. It can be used to correct any ((d*-1)/2) or fewer errors with complexity O(n/sup 3/), where d* is the designed minimum distance of the algebraic-geometric code and n is the codelength. >
248 citations
23 May 1993
TL;DR: The decoding of multidimensional product codes, using separable symbol-by-symbol maximum a posteriori filters, and the extension of the concept to concatenated convolutional codes is given and some simulation results are presented.
Abstract: Very efficient signaling in radio channels requires the design of very powerful codes having special structure suitable for practical decoding schemes. Powerful codes are obtained by using simple block codes to construct multidimensional product codes. The decoding of multidimensional product codes, using separable symbol-by-symbol maximum a posteriori filters, is described. Simulation results are presented for three-dimensional product codes constructed with the (16,11) extended Hamming code. The extension of the concept to concatenated convolutional codes is given and some simulation results are presented. Potential applications are briefly discussed. >
188 citations
TL;DR: In this paper, a determinate state convolutional code is formed from a conventional CNN by pruning away some of the possible state transitions in the decoding trellis, which is an extremely efficient way of enhancing the performance of a concatenated coding system.
Abstract: A determinate state convolutional code is formed from a conventional convolutional code by pruning away some of the possible state transitions in the decoding trellis. This staged power transfer proves to be an extremely efficient way of enhancing the performance of a concatenated coding system. The authors analyze the decoding complexity and free distances of these new codes, determine some important statistical properties of the decoder output, and provide simulation results for performance at the low signal-to-noise ratios where a real communications system would operate. Several concise, practical examples are presented. >
146 citations
TL;DR: In this paper, a generalized Dijkstra's algorithm is employed to search through a trellis for an equivalent code of the transmitted code, guided by an evaluation function f defined to take advantage of the information provided by the received vector and the inherent properties of transmitted code.
Abstract: The authors present a novel and efficient maximum-likelihood soft-decision decoding algorithm for linear block codes. The approach used here converts the decoding problem into a search problem through a graph that is a trellis for an equivalent code of the transmitted code. A generalized Dijkstra's algorithm, which uses a priority-first search strategy, is employed to search through this graph. This search is guided by an evaluation function f defined to take advantage of the information provided by the received vector and the inherent properties of the transmitted code. This function f is used to reduce drastically the search space and to make the decoding efforts of this decoding algorithm adaptable to the noise level. For example, for most real channels of the 35 000 samples tried, simulation results for the (128,64) binary extended BCH code show that the proposed decoding algorithm is fifteen orders of magnitude more efficient in time and in space than that proposed by Wolf (1978). Simulation results for the (104, 52) binary extended quadratic residue code are also given. >
145 citations
29 Nov 1993
TL;DR: An intuitive algorithm by Lodge et al.
Abstract: An intuitive algorithm by Lodge et al. [1992] for iterative decoding of block codes is shown to follow from entropy optimization principles. This approach provides a novel and effective algorithm for the soft-decoding of block codes which have a product structure. >
81 citations
TL;DR: High-speed (25-Mb/s) and universal-coding-rate Viterbi decoder VLSIs have been developed and make it possible to realize a simple and variable coding-rate forward-error-correction circuit by changing only the branch metric calculation ROM tables.
Abstract: An advanced, high-speed, and universal-coding-rate Viterbi decoder VLSI implementation is presented. Two novel circuit design schemes have been proposed: scarce state transition (SST) decoding and direct high-coding-rate convolutional code generation and variable-rate decoding. SST makes it possible to omit the final decision circuit and to reduce the required path memory length without degrading error probability performance. Moreover, the power consumption of the SST Viterbi decoder is significantly reduced when implemented as a CMOS device. These features overcome the speed limits of high-speed and high-coding-gain Viterbi decoder VLSIs in the rate one-half mode imposed by the thermal limitation. The other Viterbi decoding scheme makes it possible to realize a simple and variable coding-rate forward-error-correction circuit by changing only the branch metric calculation ROM tables. By employing these schemes, high-speed (25-Mb/s) and universal-coding-rate Viterbi decoder VLSIs have been developed. >
60 citations
TL;DR: A Reed-Solomon code decoding algorithm based on Newton's interpolation is presented, which uses a modified Berlekamp-Massey algorithm to perform all necessary generalized-minimum-distance decoding steps in only one run.
Abstract: A Reed-Solomon code decoding algorithm based on Newton's interpolation is presented. This algorithm has as main application fast generalized-minimum-distance decoding of Reed-Solomon codes. It uses a modified Berlekamp-Massey algorithm to perform all necessary generalized-minimum-distance decoding steps in only one run. With a time-domain form of the new decoder the overall asymptotic generalized-minimum-distance decoding complexity becomes O(dn), with n the length and d the distance of the code (including the calculation of all error locations and values). This asymptotic complexity is optimal. Other applications are the possibility of fast decoding of Reed-Solomon codes with adaptive redundancy and a general parallel decoding algorithm with zero delay. >
55 citations
17 Jan 1993
TL;DR: A novel maximum-likelihood soft-decision decoding algorithm for linear block codes that is adaptable to the noise level and guided by an evaluation function f to take advantage of the information provided by the received vector and the inherent properties of the transmitted code.
Abstract: In this paper we present a novel maximum-likelihood soft-decision decoding algorithm for linear block codes. The approach used here is to convert the decoding problem into a search problem through a graph which is a trellis for an equivalent code of the transmitted code. Algorithm A* is employed to search through this graph. This search is guided by an evaluation function f defined to take advantage of the information provided by the received vector and the inherent properties of the transmitted code. This function f is used to drastically reduce the search space and to make the decoding efforts of this decoding algorithm adaptable to the noise level. Simulation results for the (104, 52) binary extended quadratic residue code and the (128,64) binary extended BCH code are given.
43 citations
TL;DR: The error performance of some of these codes based on both one-stage optimum decoding and multistage suboptimum decoding has been simulated and show that these codes achieve good error performance with small decoding complexity.
Abstract: The multilevel coding technique is used for constructing multilevel trellis M-ary phase-shift-keying (MPSK) modulation codes for the Rayleigh fading channel. In the construction of a code, all the factors which affect the code performance and its decoding complexity are considered. The error performance of some of these codes based on both one-stage optimum decoding and multistage suboptimum decoding has been simulated. The simulation results show that these codes achieve good error performance with small decoding complexity. >
40 citations
29 Nov 1993
TL;DR: This work considers recursive convolutional coding as a means for constructing codes whose distance distribution is close to that obtained in the average by random coding, hence whose performance is expected to closely approach the channel capacity.
Abstract: We consider recursive convolutional coding as a means for constructing codes whose distance distribution is close to that obtained in the average by random coding, hence whose performance is expected to closely approach the channel capacity. We especially consider convolutional codes where the encoder register taps are such that it generates maximum-length sequences. Two algorithms for decoding these codes are discussed. Since both involve implementation difficulties, we propose to generate such codes by means similar to turbo-codes which make their decoding easy. >
TL;DR: The loss in quantizing coded symbols in the additive white Gaussian noise (AWGN) channel with binary phase-shift keying (BPSK) or quadrature phase- Shift keying or QPSK modulation is discussed and a quantization scheme and branch metric calculation method are presented.
Abstract: The loss in quantizing coded symbols in the additive white Gaussian noise (AWGN) channel with binary phase-shift keying (BPSK) or quadrature phase-shift keying (QPSK) modulation is discussed. A quantization scheme and branch metric calculation method are presented. For the uniformly quantized AWGN channel, cutoff rate is used to determine the step size and the smallest number of quantization bits needed for a given bit-signal-to-noise ratio (E/sub b//N/sub 0/) loss. A nine-level quantizer is presented, along with 3-b branch metrics for a rate-1/2 code, which causes an E/sub b//N/sub 0/ loss of only 0.14 dB. These results also apply to soft-decision decoding of block codes. A tight upper bound is derived for the range of path metrics in a Viterbi decoder. The calculations are verified by simulations of several convolutional codes, including the memory-14, rate-1/4 or -1/6 codes used by the big Viterbi decoders at JPL. >
29 Nov 1993
TL;DR: This paper tries to give a unified presentation of soft-output decoding algorithms, which includes the list-output Viterbi algorithm (LOVA), the soft (symbol)-output SOVA, the optimal symbol- by-symbol detector (OSSD), the optimal subblock-by-subblock detector (OBBD, "vector MAP"), and finally a SOVA based on likelihood post-processing.
Abstract: This paper tries to give a unified presentation of soft-output decoding algorithms. It is intended to be tutorial on one hand, but on the other hand it covers some recent advances as well. The presentation includes the list-output Viterbi algorithm (LOVA), the soft (symbol)-output Viterbi algorithm (SOVA), the optimal symbol-by-symbol detector (OSSD, "symbol-by-symbol MAP"), the optimal subblock-by-subblock detector (OBBD, "vector MAP"), and finally a SOVA based on likelihood post-processing. The relation between these algorithms is derived in a structured manner. The average mutual information for i.i.d. input bits is chosen as a measure for the quality of the reliability outputs. >
TL;DR: The computation and simulation results for these codes show that with multistage decoding, significant coding gains can be achieved with large reduction in decoding complexity.
Abstract: Multistage decoding of multilevel block multilevel phase-shift keying (M-PSK) modulation codes for the additive white Gaussian noise (AWGN) channel is investigated. Several types of multistage decoding, including a suboptimum soft-decision decoding scheme, are devised and analyzed. Upper bounds on the probability of an incorrect decoding of a code are derived for the proposed multistage decoding schemes. Error probabilities of some specific multilevel block 8-PSK modulation codes are evaluated and simulated. The computation and simulation results for these codes show that with multistage decoding, significant coding gains can be achieved with large reduction in decoding complexity. In one example, it is shown that the difference in performance between the proposed suboptimum multistage soft-decision decoding and the single-stage optimum decoding is small, only a fraction of a dB loss in SNR at the block error probability of 10/sup -6/. >
TL;DR: The conjecture of Rujan on error-correcting codes is proven and errors in decoding of signals transmitted through noisy channels assume the smallest values when signals are decoded at a particular finite temperature.
Abstract: The conjecture of Rujan on error-correcting codes is proven. Errors in decoding of signals transmitted through noisy channels assume the smallest values when signals are decoded at a particular finite temperature. This finite-temperature decoding is compared with the conventional maximum likelihood decoding which corresponds to the T =0 case. The method of gauge transformation in the spin glass theory is useful in this argument.
Patent•
19 Oct 1993TL;DR: In this paper, an encoding and decoding apparatus and method which has the primary benefit over the prior art of not requiring storage of the nonlinear sequence of numbers representative of the quantization characteristics was proposed.
Abstract: An encoding and decoding apparatus and method which has the primary benefit over the prior art of not requiring storage of the nonlinear sequence of numbers representative of the quantization characteristics. The hardware required for quantization is reduced and inverse quantization may be achieved using shifting operations and a multiplier of up to half the scale compared to conventional encoding/decoding methods and encoding/decoding apparatus.
20 Oct 1993
TL;DR: A concatenated decoding system employing the soft output MAP algorithm compares favorably with parallel Viterbi decoders using a standard code, which is proved by a high speed system example.
Abstract: The symbol by symbol MAP algorithm is parallelized leading to a purely feedforward block processing architecture for high speed soft output channel decoding. Using a novel algebraic formulation of the MAP algorithm, an algorithmic modification is discussed resulting a large decrease in complexity. A concatenated decoding system employing the soft output MAP algorithm compares favorably with parallel Viterbi decoders using a standard code, which is proved by a high speed system example. >
TL;DR: Bidirectional multiple-path tree searching algorithms for the decoding of convolutional codes are presented and it is shown that the bidirectional exploration considerably reduces the bit error propagation due to correct path loss.
Abstract: Bidirectional multiple-path tree searching algorithms for the decoding of convolutional codes are presented. These suboptimal coding algorithms use a multiple-path breadth-first bidirectional tree exploration procedure and long-memory convolution codes. It is shown that, compared to the usual M-algorithm, the bidirectional exploration considerably reduces the bit error propagation due to correct path loss. Computer simulations using rate-1/2 codes over binary symmetric channels are used to analyze the effect of the number of path extensions, code memory, and frame length on the bit error probability. The results show that with a bit error probability of 10/sup -5/, coding gains on the order of 2 dB over the M-algorithm and 1 dB over a Viterbi decoder of equivalent complexity can be achieved. >
TL;DR: A decoding algorithm for codes arising from algebraic curves explicitly constructable by Goppa's construction is presented and application to Hermitian codes and connections with well-known algorithms are explained.
Abstract: A decoding algorithm for codes arising from algebraic curves explicitly constructable by Goppa's construction is presented. Any configuration up to the greatest integer less than or equal to (d*-1)/2 errors is corrected by the algorithm whenever d*>or=6g, where d* is the designed minimum distance of the code and g is the genus of the curve. The algorithm's complexity is at most O((d*)/sup 2/n), where n denotes the length of the code. Application to Hermitian codes and connections with well-known algorithms are explained. >
TL;DR: Three examples from convolutional codes, matched-spectral-null (MSN) trellis codes, and Ungerboeck codes are presented to illustrate the design procedures and demonstrate the favourable area-time tradeoff results.
Abstract: In part I the theoretical foundations of a new class of area-efficient architectures for the Viterbi algorithm were established. Area-efficient architectures for practical codes are presented here to illustrate the design procedures and demonstrate the favourable area-time tradeoff results. Three examples from convolutional codes, matched-spectral-null (MSN) trellis codes, and Ungerboeck codes are presented. The application of the area-efficient techniques to codes with a very large number of states, codes with time-varying trellises, and a programmable Viterbi decoder is discussed. >
17 Jan 1993
TL;DR: It is found, by means of extensive computer simulations as well as a heuristic argument, that the advantage of the BSD appears as a substantial decrease of the computational variability of the sequential decoding.
Abstract: The main drawback of sequential decoding is the variability of its decoding effort which could cause decoding erasures. We propose and analyze an efficient bidirectional sequential decoding (BSD) technique to alleviate this drawback. In the proposed BSD, two decoders are used; one is called a forward decoder (FD), and is used to search the tree from the forward direction; while the other is called a backward decoder (BD), and is used for the backward search of the tree. Forward decoding and backward decoding are performed simultaneously, and stop whenever the FD and BD merge at a common encoder state somewhere in the tree. The relationships between backward coding and forward coding are examined in detail. Good rate 1/2 convolutional codes, with memory m ranging from 2 to 25, suitable for bidirectional decoding found through extensive computer search, are provided. These codes possess the same distance properties from both forward and backward directions. It is found, by means of extensive computer simulations as well as a heuristic argument, that the advantage of the BSD appears as a substantial decrease of the computational variability of the sequential decoding. Our findings suggest that the Pareto exponent of unidirectional sequential decoding (USD) can be practically doubled by using BSD.
TL;DR: Decoding methods for error patterns of bounded weight are described, and it is demonstrated that these methods offer a favorable combination of performance and complexity.
Abstract: We discuss minimum distance decoding of convolutional codes. The relevant distance functions are defined, and the set of correctable error patterns is described by a sequence of weight constraints. Decoding methods for error patterns of bounded weight are described, and it is demonstrated that these methods offer a favorable combination of performance and complexity. Exact values and upper bounds on the error probability are calculated from finite state models of the decoding process. >
19 Jul 1993
TL;DR: It is shown that the function fc(p) displays a threshold behaviour i.e. jumps suddenly from almost zero to almost one, and how the acuteness of the threshold effect grows with the minimal distance of C.
Abstract: A theorem of Margulis states the existence of a threshold phenomenon in the probability of disconnecting a graph, given that each of its edges is independently severed with some probability p. We show how this theorem can be reinterpreted in the coding context: in particular we study the probability fc(p) of residual error after maximum likelihood decoding, when we submit a linear code C to a binary symmetric channel with error probability p. We show that the function fc(p) displays a threshold behaviour i.e. jumps suddenly from almost zero to almost one, and how the acuteness of the threshold effect grows with the minimal distance of C. Similar results for the erasure channel are also discussed.
Patent•
07 May 1993TL;DR: In this article, a maximum likelihood decoding method is proposed for correcting burst errors caused by abrupt lowering of the signal amplitude, where the soft decision likelihood metric has a multi-valued level.
Abstract: There is provided a maximum likelihood decoding method, and an apparatus, capable of correcting burst errors caused by abrupt lowering of the signal amplitude. The soft decision maximum likelihood decoding method is a maximum likelihood decoding method for conducting maximum likelihood decoding on a received train resulting from addition of an error train to a transmission code train, which has been obtained by coding an information train by using convolutional codes on a transmission side. The soft decision maximum likelihood decoding method includes the step of making corrections by multiplying the soft decision likelihood metric having a multi-valued level, which has been obtained by soft decision likelihood metric from the received train, by weighting coefficients depending upon an instantaneous amplitude of the received signal, and the step of conducting maximum likelihood decoding by using corrected soft decision likelihood metric values. Thereby, it becomes possible to enhance the error correcting capability of error correcting apparatuses used in mobile radio communication or the like with severe fading. As a result, communication reliability is increased.
Patent•
27 Apr 1993TL;DR: An image coding/decoding apparatus intended for efficient processing by sharing members in coding, local decoding, and decoding processing is described in this article, where either of the two functions can be selected for execution in synchronization with the processing timing for each block.
Abstract: An image coding/decoding apparatus intended for efficient processing by sharing members in coding, local decoding, and decoding processing. Processes such as DCT and IDCT, zigzag scan conversion and inversion, or quantization and inverse quantization performed in coding, local decoding, and decoding processing are similar to each other. DCT/IDCT, zigzag scan conversion/inversion, and quantization/inverse quantization are provided where either of the two functions can be selected for execution in synchronization with the processing timing for each block. Since the time required for one process for data for each block is very short, overall processing is not affected even if the members are used in a time division manner. By sharing processing, the hardware scale can be made small and by using a data bus in a time division manner, an external data bus can also be eliminated.
TL;DR: New constructions of t-error correcting balanced codes, for 1>or=t>or-4, are presented, which are better than the existing codes given in the literature.
Abstract: New constructions of t-error correcting balanced codes, for 1>or=t>or=4, are presented. In a balanced code, all the words have an equal number of 1's and 0's. In many cases, the information rates of the new codes are better than the existing codes given in the literature. The proposed codes also have efficient encoding and decoding algorithms.
TL;DR: Two importance sampling techniques are presented for estimating the distribution of computation of sequential decoding for specific convolutional codes (not ensemble averages) and only stack algorithm decoders are considered.
Abstract: Two importance sampling techniques are presented for estimating the distribution of computation of sequential decoding for specific convolutional codes (not ensemble averages). Only stack algorithm decoders are considered. Numerical examples are presented for both the BSC and the AWGN channel. >
TL;DR: It is shown for coded 8-PSK that additional coding gains up to 2 dB are achieved by these means at the cost of modest complexity, but the decoding delay is increased.
Abstract: Multilevel codes give an impressive asymptotic coding gain measured in dB However, when classical multistage decoding is used, this gain can only be partly realized at bit error rates (BER) around 10−5 It is shown how multistage decoding can be improved for this BER range We use interleaving between the levels, pass reliability information between the different stages by applying “Soft-Output” decoders, and apply re-iterated decoding In the latter case lower levels are again decoded using the results of the higher levels It is shown for coded 8-PSK that additional coding gains up to 2 dB are achieved by these means at the cost of modest complexity, but the decoding delay is increased
01 Jan 1993
TL;DR: In this article, genetic algorithms for soft-decision decoding of binary linear block codes are presented. But decoding is an NP-hard problem of great interest to developers of communication systems, and this problem is equivalent to the problem of optimizing Walsh polynomials.
Abstract: Soft-decision decoding is an NP-hard problem of great interest to developers of communication systems. We show that this problem is equivalent to the problem of optimizing Walsh polynomials. We present genetic algorithms for soft-decision decoding of binary linear block codes and compare the performance with various other decoding algorithms including the currently developed A* algorithm. Simulation results show that our algorithms achieve bit-error-probabilities as low as 0.00183 for a [104,52] code with a low signal-to-noise ratio of 2.5 dB, exploring only 22,400 codewords, whereas the search space contains 4.5 10l5 codewords. We define a new crossover operator that exploits domain-specific information and compare it with uniform and two-point crossover.