Hsiao-feng Lu, Yuankai Wang, Pavan Kumar, K. Chugg
This article presents a new asymptotically exact lower bound on pairwise error probability of a space-time code as well as an example code that outperforms the comparable orthogonal-design-based space-time (ODST) code. Also contained in the article are an exact expression for pairwise error probability (PEP), signal design guidelines, and some observations relating to the reception of ODST codes.
{"title":"Remarks on space-time codes including a new lower bound and an improved code","authors":"Hsiao-feng Lu, Yuankai Wang, Pavan Kumar, K. Chugg","doi":"10.1109/TIT.2003.817475","DOIUrl":"https://doi.org/10.1109/TIT.2003.817475","url":null,"abstract":"This article presents a new asymptotically exact lower bound on pairwise error probability of a space-time code as well as an example code that outperforms the comparable orthogonal-design-based space-time (ODST) code. Also contained in the article are an exact expression for pairwise error probability (PEP), signal design guidelines, and some observations relating to the reception of ODST codes.","PeriodicalId":13250,"journal":{"name":"IEEE Trans. Inf. Theory","volume":"65 1","pages":"2752-2757"},"PeriodicalIF":0.0,"publicationDate":"2003-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83959557","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We consider the problem of list decoding from erasures. We establish lower and upper bounds on the rate of a (linear) code that can be list decoded with list size L when up to a fraction p of its symbols are adversarially erased. Our results show that in the limit of large L, the rate of such a code approaches the capacity (1 - p) of the erasure channel. Such nicely list decodable codes are then used as inner codes in a suitable concatenation scheme to give a uniformly constructive family of asymptotically good binary linear codes of rate Ω(Ɛ2/ lg(1/Ɛ)) that can be efficiently list decoded using lists of size O(1/Ɛ) from up to a fraction (1-Ɛ) of erasures. This improves previous results from [14] in this vein, which achieveda rate of Ω(Ɛ3 lg(1/Ɛ)).
{"title":"List decoding from erasures: bounds and code constructions","authors":"V. Guruswami","doi":"10.1109/TIT.2003.815776","DOIUrl":"https://doi.org/10.1109/TIT.2003.815776","url":null,"abstract":"We consider the problem of list decoding from erasures. We establish lower and upper bounds on the rate of a (linear) code that can be list decoded with list size L when up to a fraction p of its symbols are adversarially erased. Our results show that in the limit of large L, the rate of such a code approaches the capacity (1 - p) of the erasure channel. Such nicely list decodable codes are then used as inner codes in a suitable concatenation scheme to give a uniformly constructive family of asymptotically good binary linear codes of rate Ω(Ɛ2/ lg(1/Ɛ)) that can be efficiently list decoded using lists of size O(1/Ɛ) from up to a fraction (1-Ɛ) of erasures. This improves previous results from [14] in this vein, which achieveda rate of Ω(Ɛ3 lg(1/Ɛ)).","PeriodicalId":13250,"journal":{"name":"IEEE Trans. Inf. Theory","volume":"812 1","pages":"2826-2833"},"PeriodicalIF":0.0,"publicationDate":"2001-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83726516","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We establish the range of values of /spl rho/, where 0/spl les//spl rho//spl les/m(q-1), for which the generalized Reed-Muller code R/sub Fq/(/spl rho/, m) of length q/sup m/ over the field F/sub q/ of order q is spanned by its minimum-weight vectors.
{"title":"Minimum-weight codewords as generators of generalized Reed-Muller codes","authors":"Peng Ding, J. D. Key","doi":"10.1109/18.868484","DOIUrl":"https://doi.org/10.1109/18.868484","url":null,"abstract":"We establish the range of values of /spl rho/, where 0/spl les//spl rho//spl les/m(q-1), for which the generalized Reed-Muller code R/sub Fq/(/spl rho/, m) of length q/sup m/ over the field F/sub q/ of order q is spanned by its minimum-weight vectors.","PeriodicalId":13250,"journal":{"name":"IEEE Trans. Inf. Theory","volume":"141 1","pages":"2152-2158"},"PeriodicalIF":0.0,"publicationDate":"2000-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77406024","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Bandwidth-efficient multiple access (BEMA) is a strategy where transmitter pulses are continually designed at the base station and are dynamically allocated to the transmitters via a feedback channel. Such pulses (or "signature waveforms") are designed to conserve bandwidth while simultaneously enabling the receiver at the base station to meet a quality-of-service (QoS) specification for each transmitter. The key technical problem in BEMA communication is therefore the design of the transmitter pulses for the base station receiver. In an earlier paper, we presented solutions to this problem that were shown to be superior (in terms of strict bandwidth) to common signaling schemes such as time-, frequency-, and code-division multiple access (TDMA, FDMA, and CDMA). This paper uses the framework developed earlier, but considers strictly time-limited transmitter pulses and the root-mean squared (RMS) bandwidth measure. As in the earlier paper, significant bandwidth savings over the traditional multiple-access strategies are obtained. However, in contrast to the rank-conserving approach, the bandwidth gains of this paper are realized by tailoring the signature waveform design to conserve RMS bandwidth via eigenvalue optimization problems.
{"title":"Signal design for bandwidth-efficient multiple-access communications based on Eigenvalue optimization","authors":"T. Guess, M. Varanasi","doi":"10.1109/18.868477","DOIUrl":"https://doi.org/10.1109/18.868477","url":null,"abstract":"Bandwidth-efficient multiple access (BEMA) is a strategy where transmitter pulses are continually designed at the base station and are dynamically allocated to the transmitters via a feedback channel. Such pulses (or \"signature waveforms\") are designed to conserve bandwidth while simultaneously enabling the receiver at the base station to meet a quality-of-service (QoS) specification for each transmitter. The key technical problem in BEMA communication is therefore the design of the transmitter pulses for the base station receiver. In an earlier paper, we presented solutions to this problem that were shown to be superior (in terms of strict bandwidth) to common signaling schemes such as time-, frequency-, and code-division multiple access (TDMA, FDMA, and CDMA). This paper uses the framework developed earlier, but considers strictly time-limited transmitter pulses and the root-mean squared (RMS) bandwidth measure. As in the earlier paper, significant bandwidth savings over the traditional multiple-access strategies are obtained. However, in contrast to the rank-conserving approach, the bandwidth gains of this paper are realized by tailoring the signature waveform design to conserve RMS bandwidth via eigenvalue optimization problems.","PeriodicalId":13250,"journal":{"name":"IEEE Trans. Inf. Theory","volume":"46 1","pages":"2045-2058"},"PeriodicalIF":0.0,"publicationDate":"2000-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87221491","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We present analytical results relating to first- and second-moment characterization of direction dispersion and spatial selectivity in the radio channel as well as to the duality between these two effects. Dispersion in direction can be characterized either by the direction power spectrum or by a family of spatial Doppler power spectra at the reception site. Two measures called the direction spread and the maximum spatial Doppler spread are introduced which describe the extent of channel dispersion in direction and in spatial Doppler frequency, respectively. Both measures are analogous to the delay and Doppler spreads, which are commonly employed to describe the extent of dispersion in delay and Doppler frequency, respectively. The relationships between the two approaches for characterizing spatial dispersion and especially between the direction and maximum spatial Doppler spreads are analytically established. The coherence distance at a certain level summarizes certain features of space selectivity in the radio channel which impact on the performance of communication systems. Two uncertainty relations between the direction spread and the coherence distance as well as between the maximum spatial Doppler spread and the coherence distance express the duality between direction dispersion and space selectivity. These relations are analogous to those established previously between the delay spread and the coherence bandwidth and between the Doppler spread and the coherence time. Examples relevant to mobile communications in the case where the waves propagate only horizontally illustrate the theoretical results. An application of these results to the design of uniform linear antenna arrays is also discussed.
{"title":"First- and second-order characterization of direction dispersion and space selectivity in the radio channel","authors":"B. Fleury","doi":"10.1109/18.868476","DOIUrl":"https://doi.org/10.1109/18.868476","url":null,"abstract":"We present analytical results relating to first- and second-moment characterization of direction dispersion and spatial selectivity in the radio channel as well as to the duality between these two effects. Dispersion in direction can be characterized either by the direction power spectrum or by a family of spatial Doppler power spectra at the reception site. Two measures called the direction spread and the maximum spatial Doppler spread are introduced which describe the extent of channel dispersion in direction and in spatial Doppler frequency, respectively. Both measures are analogous to the delay and Doppler spreads, which are commonly employed to describe the extent of dispersion in delay and Doppler frequency, respectively. The relationships between the two approaches for characterizing spatial dispersion and especially between the direction and maximum spatial Doppler spreads are analytically established. The coherence distance at a certain level summarizes certain features of space selectivity in the radio channel which impact on the performance of communication systems. Two uncertainty relations between the direction spread and the coherence distance as well as between the maximum spatial Doppler spread and the coherence distance express the duality between direction dispersion and space selectivity. These relations are analogous to those established previously between the delay spread and the coherence bandwidth and between the Doppler spread and the coherence time. Examples relevant to mobile communications in the case where the waves propagate only horizontally illustrate the theoretical results. An application of these results to the design of uniform linear antenna arrays is also discussed.","PeriodicalId":13250,"journal":{"name":"IEEE Trans. Inf. Theory","volume":"62 1","pages":"2027-2044"},"PeriodicalIF":0.0,"publicationDate":"2000-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90838710","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A novel analytical approach to performance evaluation of soft-decoding algorithms for binary linear block codes based on probabilistic iterative error correction is presented. A convergence condition establishing the critical noise rate below which the expected bit-error probability tends to zero is theoretically derived. It explains the capability of iterative probabilistic decoding of binary linear block codes with sparse parity-check matrices to correct, with probability close to one, error patterns with the number of errors (far) beyond half the code minimum distance. Systematic experiments conducted on truncated simplex codes seem to agree well with the convergence condition. The method may also be interesting for the theoretical analysis of the so-called turbo codes.
{"title":"A method for convergence analysis of iterative probabilistic decoding","authors":"M. Mihaljević, J. Golic","doi":"10.1109/18.868493","DOIUrl":"https://doi.org/10.1109/18.868493","url":null,"abstract":"A novel analytical approach to performance evaluation of soft-decoding algorithms for binary linear block codes based on probabilistic iterative error correction is presented. A convergence condition establishing the critical noise rate below which the expected bit-error probability tends to zero is theoretically derived. It explains the capability of iterative probabilistic decoding of binary linear block codes with sparse parity-check matrices to correct, with probability close to one, error patterns with the number of errors (far) beyond half the code minimum distance. Systematic experiments conducted on truncated simplex codes seem to agree well with the convergence condition. The method may also be interesting for the theoretical analysis of the so-called turbo codes.","PeriodicalId":13250,"journal":{"name":"IEEE Trans. Inf. Theory","volume":"99 1","pages":"2206-2211"},"PeriodicalIF":0.0,"publicationDate":"2000-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85785237","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We study signal-space coding for coherent slow frequency-hopped communications over a Gaussian multiple-access collision channel (G-MACC). We define signal sets and interleavers having maximum collision resistance. The packet-error probability and the spectral efficiency obtained by these signal sets concatenated with outer block coding and hard (error-only) decoding is evaluated without assuming perfect interleaving. Closed-form expressions are provided and computer simulations show perfect agreement with analysis. The structure of good interleavers is also discussed. More generally, we present expressions for the information outage probability and for the achievable (ergodic) rate of the G-MACC at hand, under various assumptions on user coding and decoding strategies. The outage probability yields the limiting packet-error probability with finite interleaving depth (delay-limited systems). The achievable rate yields the limiting system spectral efficiency for large interleaving depth (delay-unconstrained systems). Comparisons with other classical multiple-access schemes are provided.
{"title":"Modulation and coding for the Gaussian collision channel","authors":"G. Caire, Emilio Leonardi, E. Viterbo","doi":"10.1109/18.868475","DOIUrl":"https://doi.org/10.1109/18.868475","url":null,"abstract":"We study signal-space coding for coherent slow frequency-hopped communications over a Gaussian multiple-access collision channel (G-MACC). We define signal sets and interleavers having maximum collision resistance. The packet-error probability and the spectral efficiency obtained by these signal sets concatenated with outer block coding and hard (error-only) decoding is evaluated without assuming perfect interleaving. Closed-form expressions are provided and computer simulations show perfect agreement with analysis. The structure of good interleavers is also discussed. More generally, we present expressions for the information outage probability and for the achievable (ergodic) rate of the G-MACC at hand, under various assumptions on user coding and decoding strategies. The outage probability yields the limiting packet-error probability with finite interleaving depth (delay-limited systems). The achievable rate yields the limiting system spectral efficiency for large interleaving depth (delay-unconstrained systems). Comparisons with other classical multiple-access schemes are provided.","PeriodicalId":13250,"journal":{"name":"IEEE Trans. Inf. Theory","volume":"4 1","pages":"2007-2026"},"PeriodicalIF":0.0,"publicationDate":"2000-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80207972","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We address variable-length intrinsic randomness problems (in the sense of Vembu and Verdu (1995)) for countably infinite source alphabet /spl chi/ under the (unnormalized) divergence distance, the normalized conditional divergence distance, and the variational distance. It turns out that under all three kinds of approximation measures the variable-length intrinsic randomness still takes the same value, called the inf-entropy rate of the source.
{"title":"Theorems on the variable-length intrinsic randomness","authors":"T. Han","doi":"10.1109/18.868481","DOIUrl":"https://doi.org/10.1109/18.868481","url":null,"abstract":"We address variable-length intrinsic randomness problems (in the sense of Vembu and Verdu (1995)) for countably infinite source alphabet /spl chi/ under the (unnormalized) divergence distance, the normalized conditional divergence distance, and the variational distance. It turns out that under all three kinds of approximation measures the variable-length intrinsic randomness still takes the same value, called the inf-entropy rate of the source.","PeriodicalId":13250,"journal":{"name":"IEEE Trans. Inf. Theory","volume":"57 1","pages":"2108-2116"},"PeriodicalIF":0.0,"publicationDate":"2000-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77646154","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
It is well known that an interleaver with random properties, quite often generated by pseudo-random algorithms, is one of the essential building blocks of turbo codes. However, randomly generated interleavers have two major drawbacks: lack of an adequate analysis that guarantees their performance and lack of a compact representation that leads to a simple implementation. We present several new classes of deterministic interleavers of length N, with construction complexity O(N), that permute a sequence of bits with nearly the same statistical distribution as a random interleaver and perform as well as or better than the average of a set of random interleavers. The new classes of deterministic interleavers have a very simple representation based on quadratic congruences and hence have a structure that allows the possibility of analysis as well as a straightforward implementation. Using the new interleavers, a turbo code of length 16384 that is only 0.7 dB away from capacy at a bit-error rate (BER) of 10/sup -5/ is constructed. We also generalize the theory of previously known deterministic interleavers that are based on block interleavers, and we apply this theory to the construction of a nonrandom turbo code of length 16384 with a very regular structure whose performance is only 1.1 dB away from capacity at a BER of 10/sup -5/.
{"title":"New deterministic interleaver designs for turbo codes","authors":"O. Takeshita, D. Costello","doi":"10.1109/18.868474","DOIUrl":"https://doi.org/10.1109/18.868474","url":null,"abstract":"It is well known that an interleaver with random properties, quite often generated by pseudo-random algorithms, is one of the essential building blocks of turbo codes. However, randomly generated interleavers have two major drawbacks: lack of an adequate analysis that guarantees their performance and lack of a compact representation that leads to a simple implementation. We present several new classes of deterministic interleavers of length N, with construction complexity O(N), that permute a sequence of bits with nearly the same statistical distribution as a random interleaver and perform as well as or better than the average of a set of random interleavers. The new classes of deterministic interleavers have a very simple representation based on quadratic congruences and hence have a structure that allows the possibility of analysis as well as a straightforward implementation. Using the new interleavers, a turbo code of length 16384 that is only 0.7 dB away from capacy at a bit-error rate (BER) of 10/sup -5/ is constructed. We also generalize the theory of previously known deterministic interleavers that are based on block interleavers, and we apply this theory to the construction of a nonrandom turbo code of length 16384 with a very regular structure whose performance is only 1.1 dB away from capacity at a BER of 10/sup -5/.","PeriodicalId":13250,"journal":{"name":"IEEE Trans. Inf. Theory","volume":"109 1","pages":"1988-2006"},"PeriodicalIF":0.0,"publicationDate":"2000-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72885202","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In certain memory systems the most common error is a single error and the next most common error is two errors in positions which are stored physically adjacent in the memory. In this correspondence we present optimal codes for recovering from such errors. We correct single errors and detect double adjacent errors. For detecting adjacent errors we consider codes which are byte-organized. In the binary case, it is clear that the length of the code is at most 2/sup r/-r-1, where r is the redundancy of the code. We summarize the known results and some new ones in this case. For the nonbinary case we show an upper bound, called "the pairs bound," on the length of such code. Over GF(3) codes with bytes of size 2 which attain the bound exist if and only if perfect codes with minimum Hamming distance 5 over GF(3) exist. Over GF(4) codes which attain the bound with byte size 2 exist for all redundancies. For most other parameters we prove the nonexistence of codes which attain the bound.
{"title":"Optimal codes for single-error correction, double-adjacent-error detection","authors":"M. Biberstein, T. Etzion","doi":"10.1109/18.868489","DOIUrl":"https://doi.org/10.1109/18.868489","url":null,"abstract":"In certain memory systems the most common error is a single error and the next most common error is two errors in positions which are stored physically adjacent in the memory. In this correspondence we present optimal codes for recovering from such errors. We correct single errors and detect double adjacent errors. For detecting adjacent errors we consider codes which are byte-organized. In the binary case, it is clear that the length of the code is at most 2/sup r/-r-1, where r is the redundancy of the code. We summarize the known results and some new ones in this case. For the nonbinary case we show an upper bound, called \"the pairs bound,\" on the length of such code. Over GF(3) codes with bytes of size 2 which attain the bound exist if and only if perfect codes with minimum Hamming distance 5 over GF(3) exist. Over GF(4) codes which attain the bound with byte size 2 exist for all redundancies. For most other parameters we prove the nonexistence of codes which attain the bound.","PeriodicalId":13250,"journal":{"name":"IEEE Trans. Inf. Theory","volume":"23 1","pages":"2188-2193"},"PeriodicalIF":0.0,"publicationDate":"2000-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83463512","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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