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Trellis Codes with Low Ones Density for the OR Multiple Access Channel
 In IEEE ISIT 2006
, 2006
"... Abstract — This paper presents trellis codes for the Z channel designed to maintain a relatively low ones density. These codes have applications in pulseposition modulation systems and as a solution for uncoordinated communication on the binary OR multipleaccess channel (MAC). In this paper we con ..."
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Abstract — This paper presents trellis codes for the Z channel designed to maintain a relatively low ones density. These codes have applications in pulseposition modulation systems and as a solution for uncoordinated communication on the binary OR multipleaccess channel (MAC). In this paper we consider the latter application to demonstrate the performance of the codes. The OR channel provides an unusual opportunity where singleuser decoding permits operation at about 70 % of the full multipleaccess channel sum capacity. The interleaverdivision multiple access technique applied in this paper should approach that performance with turbo solutions. However, the current paper focuses on very low latency codes with simple decoding, intended for very high speed (gigabits per second) applications. Namely, it focuses on nonlinear trellis codes that provide about 30 % of the full multipleaccess sum capacity at high speeds and with very low latency. These trellis codes are designed specifically for the ZChannel that arises in a multipleuser OR channel, when the other users are treated as noise. In order to optimize the sumcapacity of the ORMAC, the trellis code transmits codewords with a ones density much less than 50%. Also, a union bound technique that predicts the performance of these codes is presented. Results from simulations and a working FPGA implementation are shown. I.
Computation of the active distances for trellis coded modulation
 in Proceedings 5th International ITG Conference on Source and Channel Coding
, 2004
"... Recently, the concept of active distances, originally introduced for binary convolutional codes, was extended to the case of nonlinear trellis coded modulation. These distance measures allow an improved evaluation of the error correcting capability for trellis codes. Typically, the larger the slope ..."
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Recently, the concept of active distances, originally introduced for binary convolutional codes, was extended to the case of nonlinear trellis coded modulation. These distance measures allow an improved evaluation of the error correcting capability for trellis codes. Typically, the larger the slope of the active distances the better the performance of the trellis code for low . Moreover, these distance measures are of particular interest for the design of concatenated coding schemes, with respect to the choice of the inner trellis code as well as the interleaver. In this paper we present a matrix based method to compute the active distances for trellis codes in Euclidean space, encoded by an state finite state machine. The computation is based on a simplified version of the distance generating matrix, which is well known from the calculation of the distance spectrum of trellis codes. In general the distance generating matrix is of size
. We show that for trellis codes, encoded by an state FSM, the distance generating matrix can always be reduced to fiffflffi !"ff. Finally, simulation results are presented that confirm the importance of the active distances. 1
Efficient Computation of Trellis Code Generating Functions
 IEEE TRANS. COMMUN
, 2004
"... For trellis codes, generating function techniques provide the distance spectrum and a union bound on biterror rate. The computation of the generating function of a trellis code may be separated into two stages. The first stage reduces the number of states as much as possible using lowcomplexity ap ..."
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Cited by 2 (0 self)
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For trellis codes, generating function techniques provide the distance spectrum and a union bound on biterror rate. The computation of the generating function of a trellis code may be separated into two stages. The first stage reduces the number of states as much as possible using lowcomplexity approaches. The second stage produces the generating function from the reduced state diagram through some form of matrix inversion, which has a relatively high complexity. In this paper, we improve on the amount of state reduction possible during the lowcomplexity first stage. We also show that for a trellis code that is a linear convolutional code followed by a signal mapper, the number of states may always be reduced from to (( ) 2) + 1 using lowcomplexity techniques. Finally, we analytically compare the complexity of various matrix inversion techniques and verify through simulation that the twostage approach we propose has the lowest complexity. In an example, the new technique produced the union bound in about half the time required by the best algorithm already in the literature.
Nonlinear Trellis Codes for BinaryInput BinaryOutput Multiple Access Channels With SingleUser Decoding
"... This paper presents a practical solution that provides uncoordinated access to a family of BinaryInput BinaryOutput MultipleAccess Channels (BIBOMACs), including the OR channel. We propose a solution using InterleaverDivision Multiple Access (IDMA) with singleuser decoding. This solution featu ..."
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This paper presents a practical solution that provides uncoordinated access to a family of BinaryInput BinaryOutput MultipleAccess Channels (BIBOMACs), including the OR channel. We propose a solution using InterleaverDivision Multiple Access (IDMA) with singleuser decoding. This solution features Nonlinear Trellis Codes (NLTC), that permit lowcomplexity decoding in support of highspeed applications. We present a design technique for nonlinear trellis codes with controlled ones densities for binary asymmetric channels (BACs), and in particular the ZChannel, that arise in the BIBOMAC when singleuser decoding is used. Union bound techniques that predict the performance of these codes are also presented. Information theoretical calculations of the achievable sumrate of these channels are presented as well. Simulation results and from a working FPGA implementation verify the performance and feasibility of the proposed algorithm.
Constanttime algorithm for computing the Euclidean distance maps of binary images on 2D meshes with reconfigurable buses
 Information Science
, 1999
"... Abstract—We present an efficient algorithm to compute the distance spectrum of a general finite intersymbol interference (ISI) channel, whose complexity is lower than those of existing methods. Closedform expressions are derived for both input–output Euclidean distance enumerators and asymptotic di ..."
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Abstract—We present an efficient algorithm to compute the distance spectrum of a general finite intersymbol interference (ISI) channel, whose complexity is lower than those of existing methods. Closedform expressions are derived for both input–output Euclidean distance enumerators and asymptotic distance spectrum shapes for 2tap and 3tap ISI channels. Coded and/or precoded ISI channels are also discussed. Index Terms—Distance spectrum, input–output Euclidean distance enumerator (IOEDE), input–output weight enumerator, intersymbol interference (ISI) channel, precoding. I.
Further Error Event Diagram Reduction Using Algorithmic Techniques
, 2003
"... Biglieri showed that a diagram with N² states can be used to compute the generating function for any trellis code with N states. Rouanne & Costello and Zehavi & Wolf showed that for quasiregular trellis codes, an Nstate diagram produces the correct generating function. Schlegel showed that ..."
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Biglieri showed that a diagram with N² states can be used to compute the generating function for any trellis code with N states. Rouanne & Costello and Zehavi & Wolf showed that for quasiregular trellis codes, an Nstate diagram produces the correct generating function. Schlegel showed that application of a standard FSM (finitestatemachine) minimization algorithm reduces quasiregular trellis code diagrams to at most N states and often reduces the number of states for nonquasiregular trellis codes as well. In this paper we show that performing iteratively both a forward and a backward application of Schlegel's state reduction operation can further reduce the diagram produced by Schlegel's algorithm. We also upper bound the maximum required diagram size for linear trellis codes to be N 2 +1.
NonLinear Trellis Codes for Optical Applications
"... This paper presents nonlinear trellis codes that produce codewords with a relatively low density of ones. These trellis codes are designed specifically for the ZChannel that arises in a multipleuser optical channel with noncoherent combining, when the other users are treated as noise. In conjuncti ..."
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This paper presents nonlinear trellis codes that produce codewords with a relatively low density of ones. These trellis codes are designed specifically for the ZChannel that arises in a multipleuser optical channel with noncoherent combining, when the other users are treated as noise. In conjunction with interleaverdivision multiple access, these trellis codes provide a relatively low complexity solution for uncoordinated access in the optical multipleuser environment. Also, a union bound technique that predicts the performance of these codes is presented. An implementation on an FPGA is described and results are shown.
Nonlinear Turbo Codes For HigherOrder Modulations
"... ... technique for trellis coded modulation (TCM). Although this technique directly assigns constellation points to the branches of the trellis, it has been shown that the same optimal code can be accomplished by a convolutional code with a mapper that assigns a series of coded bits to a constellatio ..."
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... technique for trellis coded modulation (TCM). Although this technique directly assigns constellation points to the branches of the trellis, it has been shown that the same optimal code can be accomplished by a convolutional code with a mapper that assigns a series of coded bits to a constellation point. This notion has remained with the appearance of turbo codes. Therefore, parallel concatenated trellis coded modulation (PCTCM) has been traditionally designed using parallel concatenated convolutional codes with a bitstosymbol mapper. This paper shows that for higherorder modulations using linear codes is too restrictive. Parallel Concatenated Nonlinear Trellis Coded Modulation (PCNLTCM) which directly assigns constellation points as outputlabels to the branches of the trellis can outperform PCTCM. Simulation results are shown
InterleaverDivision Multiple Access on the OR Channel
"... Abstract — The OR channel provides an unusual opportunity where singleuser decoding permits operation at about 70 % of the full multipleaccess channel sum capacity. The interleaverdivision multiple access technique applied in this paper can approach that performance with turbo and LDPC solutions. ..."
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Abstract — The OR channel provides an unusual opportunity where singleuser decoding permits operation at about 70 % of the full multipleaccess channel sum capacity. The interleaverdivision multiple access technique applied in this paper can approach that performance with turbo and LDPC solutions. The current paper focuses on very low latency codes with simple Viterbi decoding, intended for very high speed (gigabits per second) applications. Namely, it focuses on nonlinear trellis codes that provide about 30 % of the full multipleaccess sum capacity at high speeds and with very low latency. These trellis codes are designed specifically for the Zchannel that arises in a multipleuser OR channel when the other users are treated as noise. In order to optimize the sumcapacity of the ORMAC, the trellis code transmits codewords with a ones density much less than 50%. Also, a union bound technique that predicts the performance of these codes is presented. Results from simulations and an awardwinning FPGA implementation are shown. I.