A construction of uniquely decodable codes for the two-user binary adder channel is presented. The rates of the codes obtained by this construction are greater than the rates guaranteed by the Coebergh van den Braak and van Tilborg construction and these codes can be used with simple encoding and decoding procedures.
提出了一种双用户二进制加法器信道唯一可解码码的构造方法。这种结构获得的码率大于Coebergh van den Braak和van Tilborg结构所保证的码率，并且这些码可以用简单的编码和解码程序使用。
{"title":"Construction of Uniquely Decodable Codes for the Two-User Binary Adder Channel","authors":"R. Ahlswede, V. Balakirsky","doi":"10.1109/18.746834","DOIUrl":"https://doi.org/10.1109/18.746834","url":null,"abstract":"A construction of uniquely decodable codes for the two-user binary adder channel is presented. The rates of the codes obtained by this construction are greater than the rates guaranteed by the Coebergh van den Braak and van Tilborg construction and these codes can be used with simple encoding and decoding procedures.","PeriodicalId":13250,"journal":{"name":"IEEE Trans. Inf. Theory","volume":"44 1","pages":"326-330"},"PeriodicalIF":0.0,"publicationDate":"1999-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86208313","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}
Arikan and Merhav (1998) studied the problem of guessing a random vector X within distortion D, and characterized the best attainable exponent E(D,/spl rho/) of the /spl rho/th moment of the number of required guesses G(X) until the guessing error falls below D. We extend these results to a multistage, hierarchical guessing model, which allows for a faster search for a codeword vector at the encoder of a rate-distortion codebook. In the two-stage case of this model, if the target distortion level is D/sub 2/, the guesser first makes guesses with respect to (a higher) distortion level D/sub 1/, and then, upon his/her first success, directs the subsequent guesses to distortion D/sub 2/. As in the above-mentioned earlier paper, we provide a single-letter characterization of the best attainable guessing exponent, which relies heavily on well-known results on the successive refinement problem. We also relate this guessing exponent function to the source-coding error exponent function of the two-step coding process.
{"title":"Hierarchical Guessing with a Fidelity Criterion","authors":"N. Merhav, R. Roth, E. Arıkan","doi":"10.1109/18.746836","DOIUrl":"https://doi.org/10.1109/18.746836","url":null,"abstract":"Arikan and Merhav (1998) studied the problem of guessing a random vector X within distortion D, and characterized the best attainable exponent E(D,/spl rho/) of the /spl rho/th moment of the number of required guesses G(X) until the guessing error falls below D. We extend these results to a multistage, hierarchical guessing model, which allows for a faster search for a codeword vector at the encoder of a rate-distortion codebook. In the two-stage case of this model, if the target distortion level is D/sub 2/, the guesser first makes guesses with respect to (a higher) distortion level D/sub 1/, and then, upon his/her first success, directs the subsequent guesses to distortion D/sub 2/. As in the above-mentioned earlier paper, we provide a single-letter characterization of the best attainable guessing exponent, which relies heavily on well-known results on the successive refinement problem. We also relate this guessing exponent function to the source-coding error exponent function of the two-step coding process.","PeriodicalId":13250,"journal":{"name":"IEEE Trans. Inf. Theory","volume":"62 1","pages":"330-337"},"PeriodicalIF":0.0,"publicationDate":"1999-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83991296","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 slotted, dual-bus systems, M stations are connected to two unidirectional buses in a linear order and transmissions use slots passing through the stations. If a slot is used by a station i to transmit to a station j, j>i, then the slot can be reused by a station k, k/spl ges/j. We show that the necessary and sufficient length of addresses for full slot reuse is M-2 bits for w=0 and [(M-1)/2/sup w-1/]+w-2 bits for w/spl ges/1 and M>1+2/sup w/, where w is the bit delay at every station.
{"title":"On the Relation Between Bit Delay for Slot Reuse and the Number of Address Bits in the Dual-Bus Configuration","authors":"O. Sharon","doi":"10.1109/18.746844","DOIUrl":"https://doi.org/10.1109/18.746844","url":null,"abstract":"In slotted, dual-bus systems, M stations are connected to two unidirectional buses in a linear order and transmissions use slots passing through the stations. If a slot is used by a station i to transmit to a station j, j>i, then the slot can be reused by a station k, k/spl ges/j. We show that the necessary and sufficient length of addresses for full slot reuse is M-2 bits for w=0 and [(M-1)/2/sup w-1/]+w-2 bits for w/spl ges/1 and M>1+2/sup w/, where w is the bit delay at every station.","PeriodicalId":13250,"journal":{"name":"IEEE Trans. Inf. Theory","volume":"32 1","pages":"356-365"},"PeriodicalIF":0.0,"publicationDate":"1999-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88807185","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}
Source coding theorems for general sources are presented. For a source /spl mu/, which is assumed to be a probability measure on all strings of an infinite-length sequence with a finite alphabet, the notion of almost-sure sup entropy rate is defined; it is an extension of the Shannon entropy rate. When both an encoder and a decoder know that a sequence is generated by /spl mu/, the following two theorems can be proved: (1) in the almost-sure sense, there is no variable-rate source coding scheme whose coding rate is less than the almost-sure sup entropy rate of /spl mu/, and (2) in the almost-sure sense, there exists a variable-rate source coding scheme whose coding rate achieves the almost-sure sup entropy rate of /spl mu/.
{"title":"Almost-Sure Variable-Length Source Coding Theorems for General Sources","authors":"J. Muramatsu, F. Kanaya","doi":"10.1109/18.746838","DOIUrl":"https://doi.org/10.1109/18.746838","url":null,"abstract":"Source coding theorems for general sources are presented. For a source /spl mu/, which is assumed to be a probability measure on all strings of an infinite-length sequence with a finite alphabet, the notion of almost-sure sup entropy rate is defined; it is an extension of the Shannon entropy rate. When both an encoder and a decoder know that a sequence is generated by /spl mu/, the following two theorems can be proved: (1) in the almost-sure sense, there is no variable-rate source coding scheme whose coding rate is less than the almost-sure sup entropy rate of /spl mu/, and (2) in the almost-sure sense, there exists a variable-rate source coding scheme whose coding rate achieves the almost-sure sup entropy rate of /spl mu/.","PeriodicalId":13250,"journal":{"name":"IEEE Trans. Inf. Theory","volume":"116 1","pages":"337-342"},"PeriodicalIF":0.0,"publicationDate":"1999-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86213765","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 give direct and recursive constructions for aperiodic and periodic complementary sequences. Using these constructions, many missing entries in the table of Bomer and Antweiler (1990) can be filled.
{"title":"On Aperiodic and Periodic Complementary Binary Sequences","authors":"K. Feng, P. Shiue, Qing Xiang","doi":"10.1109/18.746823","DOIUrl":"https://doi.org/10.1109/18.746823","url":null,"abstract":"We give direct and recursive constructions for aperiodic and periodic complementary sequences. Using these constructions, many missing entries in the table of Bomer and Antweiler (1990) can be filled.","PeriodicalId":13250,"journal":{"name":"IEEE Trans. Inf. Theory","volume":"64 1","pages":"296-303"},"PeriodicalIF":0.0,"publicationDate":"1999-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72765542","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 upper bounds of the finite blocklength capacity C/sub n,FB/(P) of the discrete time Gaussian channel with feedback. We also let C/sub n/(p) be the nonfeedback capacity. We prove the relations C/sub n/(P)/spl les/C/sub n,FB/(P)/spl les/C/sub n/(/spl alpha/P)+ 1/2 ln(1+1//spl alpha/) and C/sub n/(P)/spl les/C/sub n,FB/(P)/spl les/(1+1//spl alpha/)C/sub n/(/spl alpha/P) for any P>0 and any /spl alpha/>0, which induce the half-bit and factor-of-two bounds given by Cover and Pombra (1989) in the special case of /spl alpha/=1.
{"title":"Refinements of the Half-Bit and Factor-of-Two Bounds for Capacity in Gaussian Channel with Feedback","authors":"H. Chen, K. Yanagi","doi":"10.1109/18.746831","DOIUrl":"https://doi.org/10.1109/18.746831","url":null,"abstract":"We consider the upper bounds of the finite blocklength capacity C/sub n,FB/(P) of the discrete time Gaussian channel with feedback. We also let C/sub n/(p) be the nonfeedback capacity. We prove the relations C/sub n/(P)/spl les/C/sub n,FB/(P)/spl les/C/sub n/(/spl alpha/P)+ 1/2 ln(1+1//spl alpha/) and C/sub n/(P)/spl les/C/sub n,FB/(P)/spl les/(1+1//spl alpha/)C/sub n/(/spl alpha/P) for any P>0 and any /spl alpha/>0, which induce the half-bit and factor-of-two bounds given by Cover and Pombra (1989) in the special case of /spl alpha/=1.","PeriodicalId":13250,"journal":{"name":"IEEE Trans. Inf. Theory","volume":"31 6 1","pages":"319-325"},"PeriodicalIF":0.0,"publicationDate":"1999-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89766755","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 introduce a form of the Hopfield model that is able to store an increasing number of biased i.i.d. patterns (it is well known that the standard Hopfield model fails to work properly in this context). We show that this new form of the Hopfield model with N neurons can store (N)/(/spl gamma/ log N) or /spl alpha/N biased patterns (depending on which notion of storage is used). The quantity /spl gamma/ increases with an increasing bias of the patterns, while /spl alpha/ decreases when the bias gets large.
{"title":"On the Storage Capacity of the Hopfield Model with Biased Patterns","authors":"Matthias Löwe","doi":"10.1109/18.746829","DOIUrl":"https://doi.org/10.1109/18.746829","url":null,"abstract":"We introduce a form of the Hopfield model that is able to store an increasing number of biased i.i.d. patterns (it is well known that the standard Hopfield model fails to work properly in this context). We show that this new form of the Hopfield model with N neurons can store (N)/(/spl gamma/ log N) or /spl alpha/N biased patterns (depending on which notion of storage is used). The quantity /spl gamma/ increases with an increasing bias of the patterns, while /spl alpha/ decreases when the bias gets large.","PeriodicalId":13250,"journal":{"name":"IEEE Trans. Inf. Theory","volume":"74 1","pages":"314-318"},"PeriodicalIF":0.0,"publicationDate":"1999-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85596661","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}
The generalized write-once memory introduced by Fiat and Shamir (1984) is a q-ary information storage medium. Each storage cell is expected to store one of q symbols, and the legal state transitions are described by an arbitrary directed acyclic graph. This memory model can be understood as a generalization of the binary write-once memory which was introduced by Rivest and Shamir (1982). During the process of updating information, the contents of a cell can be changed from a 0-state to a 1-state but not vice versa. We study the problem of reusing a generalized write-once memory for T successive cycles (generations). We determine the zero-error capacity region and the maximum total number of information hits stored in the memory for T consecutive cycles for the situation where the encoder knows and the decoder does not know the previous state of the memory. These results extend the results of Wolf, Wyner, Ziv, and Korner (1984) for the binary write-once memory.
由Fiat和Shamir(1984)提出的广义一次写入存储器是一种q元信息存储介质。每个存储单元期望存储q个符号中的一个，并且合法的状态转换由任意有向无环图描述。这种内存模型可以理解为Rivest和Shamir(1982)引入的二进制一次写入内存的推广。在更新信息的过程中，单元格的内容可以从0状态更改为1状态，反之则不行。研究了T个连续周期(代)的通用一次写入内存的重用问题。在编码器知道而解码器不知道存储器先前状态的情况下，我们确定了零错误容量区域和存储在存储器中连续T个周期的信息命中的最大总数。这些结果扩展了Wolf, Wyner, Ziv, and Korner(1984)关于二进制一次写入存储器的结果。
{"title":"On the Capacity of Generalized Write-Once Memory with State Transitions Described by an Arbitrary Directed Acyclic Graph","authors":"Fang-Wei Fu, Han Vinck","doi":"10.1109/18.746827","DOIUrl":"https://doi.org/10.1109/18.746827","url":null,"abstract":"The generalized write-once memory introduced by Fiat and Shamir (1984) is a q-ary information storage medium. Each storage cell is expected to store one of q symbols, and the legal state transitions are described by an arbitrary directed acyclic graph. This memory model can be understood as a generalization of the binary write-once memory which was introduced by Rivest and Shamir (1982). During the process of updating information, the contents of a cell can be changed from a 0-state to a 1-state but not vice versa. We study the problem of reusing a generalized write-once memory for T successive cycles (generations). We determine the zero-error capacity region and the maximum total number of information hits stored in the memory for T consecutive cycles for the situation where the encoder knows and the decoder does not know the previous state of the memory. These results extend the results of Wolf, Wyner, Ziv, and Korner (1984) for the binary write-once memory.","PeriodicalId":13250,"journal":{"name":"IEEE Trans. Inf. Theory","volume":"9 1","pages":"308-313"},"PeriodicalIF":0.0,"publicationDate":"1999-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76557740","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}
The high-order ambiguity function (HAF) was introduced for the estimation of polynomial-phase signals (PPS) embedded in noise. Since the HAF is a nonlinear operator, it suffers from noise-masking effects and from the appearance of undesired cross terms and, possibly, spurious harmonics in the presence of multicomponent (mc) signals. The product HAF (PHAF) was then proposed as a way to improve the performance of the HAF in the presence of noise and to solve the ambiguity problem. In this correspondence we derive a statistical analysis of the PHAF in the presence of additive white Gaussian noise (AWGN) valid for high signal-to-noise ratio (SNR) and a finite number of data samples. The analysis is carried out in detail for single-component PPS but the multicomponent case is also discussed. Error propagation phenomena implicit in the recursive structure of the PHAF-based estimator are explicitly taken into account. The analysis is validated by simulation results for both single- and multicomponent PPSs.
{"title":"Statistical Analysis of the Product High-Order Ambiguity Function","authors":"A. Scaglione, S. Barbarossa","doi":"10.1109/18.746840","DOIUrl":"https://doi.org/10.1109/18.746840","url":null,"abstract":"The high-order ambiguity function (HAF) was introduced for the estimation of polynomial-phase signals (PPS) embedded in noise. Since the HAF is a nonlinear operator, it suffers from noise-masking effects and from the appearance of undesired cross terms and, possibly, spurious harmonics in the presence of multicomponent (mc) signals. The product HAF (PHAF) was then proposed as a way to improve the performance of the HAF in the presence of noise and to solve the ambiguity problem. In this correspondence we derive a statistical analysis of the PHAF in the presence of additive white Gaussian noise (AWGN) valid for high signal-to-noise ratio (SNR) and a finite number of data samples. The analysis is carried out in detail for single-component PPS but the multicomponent case is also discussed. Error propagation phenomena implicit in the recursive structure of the PHAF-based estimator are explicitly taken into account. The analysis is validated by simulation results for both single- and multicomponent PPSs.","PeriodicalId":13250,"journal":{"name":"IEEE Trans. Inf. Theory","volume":"138 1","pages":"343-356"},"PeriodicalIF":0.0,"publicationDate":"1999-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76022228","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}
For original paper see Feder and Merhav (IEEE Trans. Inform. Theory, vol.40, p.259-66, 1994 January). The present authors discuss the upper and lower bounds on the equivocation in terms of the Bayes error probability.
{"title":"Comment on 'Relations Between Entropy and Error Probability'","authors":"J. Golic","doi":"10.1109/18.746849","DOIUrl":"https://doi.org/10.1109/18.746849","url":null,"abstract":"For original paper see Feder and Merhav (IEEE Trans. Inform. Theory, vol.40, p.259-66, 1994 January). The present authors discuss the upper and lower bounds on the equivocation in terms of the Bayes error probability.","PeriodicalId":13250,"journal":{"name":"IEEE Trans. Inf. Theory","volume":"57 1","pages":"372"},"PeriodicalIF":0.0,"publicationDate":"1999-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73123005","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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