We investigate the computation of Csiszar's bounds for the joint source-channel coding (JSCC) error exponent E-J of a communication system consisting of a discrete memoryless source and a discrete memoryless chann...
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We investigate the computation of Csiszar's bounds for the joint source-channel coding (JSCC) error exponent E-J of a communication system consisting of a discrete memoryless source and a discrete memoryless channel. We provide equivalent expressions for these bounds and derive explicit formulas for the rates where the bounds are attained. These equivalent representations can be readily computed for arbitrary source-channel pairs via Arimoto's algorithm. When the channel's distribution satisfies a symmetry property, the bounds admit closed-form parametric expressions. We then use our results to provide a systematic comparison between the JSCC error exponent E-J and the tandem coding error exponent E-T, which applies if the source and channel are separately coded. It is shown that E-T <= E-J <= 2E(T). We establish conditions for which E-J > E-T and for which E-J = 2E(T). Numerical examples indicate that E-J is close to 2E(T) for many source-channel pairs. This gain translates into a power saving larger than 2 dB for a binary source transmitted over additive white Gaussian noise (AWGN) channels and Rayleigh-fading channels with finite output quantization. Finally, we study the computation of the lossy JSCC error exponent under the Hamming distortion measure.
The cutoff rate R-0 (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 W-1, W-2, the c...
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The cutoff rate R-0 (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 W-1, W-2, the capacity function always satisfies C(W-1) + C(W-2): <= C(W), while there are examples for which R-0 (W-1) + R-0 (W-2) > R-0 (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.
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