Multiple accessing for the collision channel without feedback

We consider asynchronous multiple accessing without feedback over the collision channel. Redundant coding is used to overcome user interference which causes erasures for collided packets. The channel has a sum capacity of e^-1and a sum cutoff rate of 0.295. The best codes are long constraint length rate 1/3 convolutional encoders which achieve a sum throughput up to the sum cutoff rate using an easy-to-implement forward search decoding algorithm. In the presence of additive Gaussian noise, the same redundant coding can save, at hardly any extra cost, about 6 dB of signal-to-noise ratio.     

Capacity, Cutoff Rate, and Coding for a Direct-Detection Optical Channel

It is shown that When Pierce's pulse-position modulation scheme with 2^Lpositions is used on a self-noise-limited directdetection optical communication channel, there results a 2^L-ary erasure channel that is equivalent to the parallel combination ofL"completely correlated" binary erasure channels. The capacity of the full channel is the sum of the capacities of the component channels, but the cutoff rate of the full channel is shown to be much smaller than the sum of the cutoff rates. An interpretation of the cutoff rate is given that suggests a complexity advantage in coding separately on the component channels. It is shown that if short-constraint length convolutional codes with Viterbi decoders are used on the component channels, then the performance and complexity compare favorably with the Reed-Solomon coding system proposed by McEliece for the full channel. The reasons for this unexpectedly fine performance by the convolutional code system are explored in detail, as are various facets of the channel structure.     

Channel combining and splitting for cutoff rate improvement

The cutoff rate R₀(W) of a discrete memoryless channel (DMC) W is often used as a figure of merit alongside the channel capacity C(W). If a channel W is split into two possibly correlated subchannels W₁, W₂, the capacity function always satisfies C(W₁)+C(W₂)lesC(W), while there are examples for which R₀(W₁)+R₀(W₂ )>R₀(W). The fact that cutoff rate can be "created" by channel splitting was noticed by Massey in his study of an optical modulation system. This paper gives a general framework for achieving similar gains in the cutoff rate of arbitrary DMCs by methods of channel combining and splitting. The emphasis is on simple schemes that can be implemented in practice. We give several examples that achieve significant gains in cutoff rate at little extra system complexity. Theoretically, as the complexity grows without bound, the proposed framework is capable of boosting the cutoff rate of a channel to arbitrarily close to its capacity in a sense made precise in the paper. Apart from Massey's work, the methods studied here have elements in common with Forney's concatenated coding idea, a method by Pinsker for cutoff rate improvement, and certain coded-modulation techniques, namely, Ungerboeck's set-partitioning idea and Imai-Hirakawa multilevel coding; these connections are discussed in the paper     

On the generalized symmetric cutoff rate for finite-state channels

Finite-state discrete-time channels with equiprobable M-ary inputs are considered. The generating function bound, which is ubiquitously applied to upper-bound the error probability of uncoded signaling over these channels, is used here to lower-bound the corresponding generalized symmetric cutoff rate, which lower-bounds the practically achievable rates and error exponents in these channels with symmetric signaling. The bound accounts for general additive metrics. For the special case of the optimal maximum-likelihood metric, the corresponding bound is shown to be asymptotically tight in the region where the symmetric cutoff rate approaches its maximum value of log₂ M (bits-per-channel use). For a finite-state additive white Gaussian noise (AWGN) channel this feature is used to relate the minimum Euclidean distance of an uncoded symmetric system to the corresponding symmetric cutoff rate. The results are demonstrated for AWGN channels corrupted by linear and nonlinear intersymbol interference. They are also used to assess the efficiency of concatenated coding over the 4-ary AWGN channel where the finite-state mechanism is defined by simple rate 1/2, four-state Ungerboeck 4-AM trellis code     

Throughput analysis for code division multiple accessing of the spread spectrum channel

We consider the use of error correction codes of rate r on top of pseudonoise (PN) sequence coding for code division multiple accessing of the spread spectrum channel. The channel is found to have a maximum throughput of 0.72 and 0.36 based on the evaluation of channel capacity and cutoff rate, respectively. More generally, these two values are derived for given bandwidth expanding n/r versus n/N where n is the length of the PN sequence and N is the number of Simultaneous users. It is found that to achieve the maximum throughput, n should be small. This implies that coding schemes with short PN sequences and low rate codes are superior in terms of throughput or antijam capability. The extreme case of n = 1 corresponds to using a very low rate code with no PN sequence coding. Convolutional codes are recommended and analyzed for their error rate and decoding complexity.     

A direct geometrical method for bounding the error exponent for anyspecific family of channel codes. I. Cutoff rate lower bound for blockcodes

A direct, general, and conceptually simple geometrical method for determining lower and upper bounds on the error exponent of any specific family of channel block codes is presented. It is considered that a specific family of codes is characterized by a unique distance distribution exponent. The tight linear lower bound of slope -1 on the code family error exponent represents the code family cutoff rate bound. It is always a minimum of a sum of three functions. The intrinsic asymptotic properties of channel block codes are revealed by analyzing these functions and their relationships. It is shown that the random coding technique for lower-bounding the channel error exponent is a special case of this general method. The requirements that a code family should meet in order to have a positive error exponent and at best attain the channel error exponent are stated in a clear way using the (direct) distance distribution method presented     

Throughput Analysis for Code Division Multiple Accessing of the Spread Spectrum Channel

We consider the use of error correction codes of rateron top of pseudonoise (PN) sequence coding for code division multiple accessing of the spread spectrum channel. The channel is found to have a maximum throughput of 0.72 and 0.36 based on the evaluation of channel capacity and cutoff rate, respectively. More generally, these two values are derived for given bandwidth expandingn/rversusn/Nwherenis the length of the PN sequence andNis the number of simultaneous users. It is found that to achieve the maximum throughput,nshould be small. This implies that coding schemes with short PN sequences and low rate codes are superior in terms of throughput or antijam capability. The extreme case ofn = 1corresponds to using a very low rate code with no PN sequence coding. Convolutional codes are recommended and analyzed for their error rate and decoding complexity.     

衰落信道上TAS/MRC的错误指数

使用梅哲-G 函数,推导了Nakagami-m 衰落发射天线选择（TAS）/最大比合并（MRC）系统的随机编码错误指数（RCEE）、遍历容量、截止速率、删改指数的精确表达式。计算结果表明,Nakagami-m衰落TAS/MRC系统的错误指数与信道衰落参数、信道编码速率、收发天线数目、信道相干时间等因素有关。信道衰落系数越大、编码速率越大、收发天线数目越多,通信系统的RCEE越大,相应的译码错误概率越小,系统的通信可靠性越高。对于给定译码错误概率的MIMO无线通信系统,可以通过计算系统的RCEE来估计信道所需的编码长度、收发天线数目、信道相干时间和空间衰落相关时的编码需求。     

无线通信中的空时编码技术

在第3代移动通信系统中,空时编码(space-time coding)技术是抗信道衰落和提高系统容量的一种最新编码方法。文章综述空时编码技术的产生、基本原理和应用简况,并分别介绍三种空时编码方法的特点。     

Performance of fast frequency hopped noncoherent MESK witha fixed hop rate under worst case jamming

The performance of fast-frequency-hopped M-ary frequency-shift keying with a fixed hop rate is evaluated, utilizing the Chernoff union bound method. The performance criterion used is a throughput measure i.e., an information rate sustained by a system for a given bit error rate, normalized by the hop rate. Both uncoded and coded systems are considered. It is shown using the cutoff rate argument that coding can provide a few dB gain in throughput. This is confirmed by the performance evaluation of various convolutional and block codes. Both partial-band noise jamming and multitone jamming with one tone per M -ary band are considered. Jamming parameters are assumed to be the worst case against the coding channel. Determination of the optimum M is also addressed     

Probabilistic construction of large constraint length trellis codesfor sequential decoding

Probabilistic algorithms are given for constructing good large constraint length trellis codes for use with sequential decoding that can achieve the channel cutoff rate bound at a bit error rate (BER) of 10^-5-10^-6. The algorithms are motivated by the random coding principle that an arbitrary selection of code symbols will produce a good code with high probability. One algorithm begins by choosing a relatively small set of codes randomly. The error performance of each of these codes is evaluated using sequential decoding and the code with the best performance among the chosen set is retained. Another algorithm treats the code construction as a combinatorial optimization problem and uses simulated annealing to direct the code search. Trellis codes for 8 PSK and 16 QAM constellations with constraint lengths v up to 20 are obtained. Simulation results with sequential decoding show that these codes reach the channel cutoff rate bound at a BER of 10^-5-10^-6 and achieve 5.0-6.35 dB real coding gains over uncoded systems with the same spectral efficiency and up to 2.0 dB real coding gains over 64 state trellis codes using Viterbi decoding     

Forward link capacity limit of coded FFH/CDMA multiuser mobile radios

The theoretical limit of the forward link (base to mobile) user capacity of fast frequency hopping code division multiple access (FFH/CDMA) mobile communication systems with error correction coding is investigated. The channel cutoff rate of coded FFH/CDMA channels is calculated and the optimal code rate that maximises the user capacity is determined. It is shown that with deletion-free transmission, the frequency efficiency of an FFH/CDMA channel coded at the optimal code rate is 47% higher than without coding.<>     

Duality bounds on the cutoff rate with applications to Ricean fading

We propose a technique to derive upper bounds on Gallager's cost-constrained random coding exponent function. Applying this technique to the noncoherent peak-power or average-power limited discrete time memoryless Ricean fading channel, we obtain the high signal-to-noise ratio (SNR) expansion of this channel's cutoff rate. At high SNR, the gap between channel capacity and the cutoff rate approaches a finite limit. This limit is approximately 0.26 nats per channel-use for zero specular component (Rayleigh) fading and approaches 0.39 nats per channel-use for very large values of the specular component. We also compute the asymptotic cutoff rate of a Rayleigh-fading channel when the receiver has access to some partial side information concerning the fading. It is demonstrated that the cutoff rate does not utilize the side information as efficiently as capacity, and that the high SNR gap between the two increases to infinity as the imperfect side information becomes more and more precise.     

The two-user cutoff rate for an asynchronous and a synchronous multiple-access channel are the same

The cutoff rate region for block coding of a two-sender one-receiver multiple-access channel is shown to be the same with and without frame synchronization between the two senders.     

Design of a low-orbit-to-geostationary satellite link for maximalthroughput

We examine the design of a communication link involving the data transfer from a small, low-orbit satellite to a ground station, but through a geostationary satellite. The advantage of this approach is that a single ground station, which tracks only the geostationary satellite, may be shared by a multiplicity of small satellites. Our goal is to select certain small satellite parameters-signaling rate, small satellite antenna beamwidth, modulation scheme and coding scheme-which maximize the data throughput in bits/day. Our approach uses orbital simulations of this scenario together with theoretical analysis based on the channel capacity and cutoff rate. The throughput achievable by several practical coding schemes is also examined     

Sequential decoding with ARQ and code combining: a robust hybridFEC/ARQ system

Sequential decoding with ARQ (automatic-repeat-request) and code combining under the timeout condition is considered. That is, whenever the decoding time of a given packet exceeds some predetermined duration, decoding is stopped and retransmission of the packet is requested. However, the unsuccessful packets are not discarded, but are combined with their retransmitted copies. It is shown that the use of code combining allows sequential decoding to operate efficiently even when the coding rate R exceeds the computational cutoff rate R _comp. Furthermore, an analysis of the selective-repeat ARQ scheme shows that the use of code combining yields a significant throughput even at very high channel error rates, thus making the system very robust under severe degradations of the channel     

Capacity and coding for the Gilbert-Elliot channels

The Gilbert-Elliott channel, a varying binary symmetric channel, with crossover probabilities determined by a binary-state Markov process, is treated. In general, such a channel has a memory that depends on the transition probabilities between the states. A method of calculating the capacity of this channel is introduced and applied to several examples, and the question of coding is addressed. In the conventional usage of varying channels, a code suitable for memoryless channels is used in conjunction with an interleaver, with the decoder considering the deinterleaved symbol stream as the output of a derived memoryless channel. The transmission rate is limited by the capacity of this memoryless channel, which is often considerably less than the capacity of the original channel. A decision-feedback decoding algorithm that completely recovers this capacity loss is introduced. It is shown that the performance of a system incorporating such an algorithm is determined by an equivalent genie-aided channel, the capacity of which equals that of the original channel. The calculated random coding exponent of the genie-aided channel indicates a considerable increase in the cutoff rate over that of the conventionally derived memoryless channel     

Repeated convolutional codes for high-error-rate channels

An error-correction scheme for an M-ary symmetric channel (MSC) characterized by a large error probability p_e is considered. The value of p_e can be near, but smaller than, 1-1/M, for which the channel capacity is zero, such as may occur in a jamming environment. The coding scheme consists of an outer convolutional code and an inner repetition code of length m that is used for each convolutional code symbol. At the receiving end, the m inner code symbols are used to form a soft-decision metric, which is passed to a soft-decision decoder for the convolutional code. The effect of finite quantization and methods to generate binary metrics for M>2 are investigated. Monte Carlo simulation results are presented. For the binary symmetric channel (BSC), it is shown that the overall code rate is larger than 0.6R₀, where R₀ is the cutoff rate of the channel. New union bounds on the bit error probability for systems with a binary convolutional code on 4-ary and 8-ary orthogonal channels are presented. For a BSC and a large m, a method is presented for BER approximation based on the central limit theorem     

On the cutoff rate of a discrete memoryless channel with(d, k)-constrained input sequences

The cutoff rate of a discrete memoryless channel whose output sequences are from a (d, k) encoder is investigated. A rational rate (d, k) encoder is considered as a finite state machine and maximum-likelihood decoding is used to compute the cutoff rate. Some commonly used (d, k) codes, such as the rate 1/2 (1, 3) code with a two-state encoder, the IBM rate 2/3 (1, 7) code having a five-state encoder, and the IBM rate 1/2 (2, 7) code with a seven-state encoder, are used to illustrate the cutoff rate computation. Results are presented for both the binary symmetric channel (BSC) and the Gaussian noise channel. The performance of a decoder designed for noiseless transmission of (1, 3) code is compared to that of a maximum-likelihood decoder for the (1, 3) code. It is also shown that for the case of the Gaussian noise channel, a gain of about 1.7 dB in signal-to-noise ratio is possible by using 3-bit soft decisions over hard decisions     

Direct sum DC-free coding schemes for multi-user adder channel

The design of uniquely decodable multi-user coding schemes with good rate sums for the DC-free multiple access adder channel is described. By using the direct sum construction on short multi-user codes, it is possible to devise longer DC-free coding schemes with rate sums which increase quite rapidly at each iteration of the construction. Asymptotically, there is no penalty in requiring the coding schemes to be DC-free. In addition, the schemes can be efficiently soft decision decoded using a relatively low complexity sectionalised trellis