Abstract-We investigate the joint source-channel coding problem of transmitting nonuniform memoryless sources over binary phase-shift keying-modulated additive white Gaussian noise and Rayleigh fading channels via turbo codes. In contrast to previous work, recursive nonsystematic convolutional encoders are proposed as the constituent encoders for heavily biased sources. We prove that under certain conditions, and when the length of the input source sequence tends to infinity, the encoder state distribution and the marginal output distribution of each constituent recursive convolutional encoder become asymptotically uniform, regardless of the degree of source nonuniformity. We also give a conjecture (which is empirically validated) on the condition for the higher order distribution of the encoder output to be asymptotically uniform, irrespective of the source distribution. Consequently, these conditions serve as design criteria for the choice of good encoder structures. As a result, the outputs of our selected nonsystematic turbo codes are suitably matched to the channel input, since a uniformly distributed input maximizes the channel mutual information, and hence, achieves capacity. Simulation results show substantial gains by the nonsystematic codes over previously designed systematic turbo codes; furthermore, their performance is within 0.74-1.17 dB from the Shannon limit. Finally, we compare our joint source-channel coding system with two tandem schemes which employ a fourth-order Huffman code (performing near-optimal data compression) and a turbo code that either gives excellent waterfall bit-error rate (BER) performance or good error-floor performance. At the same overall transmission rate, our system offers robust and superior performance at low BERs ( 10 4 ), while its complexity is lower.Index Terms-Additive white Gaussian noise (AWGN) and Rayleigh fading channels, joint source-channel coding, nonsystematic turbo codes, nonuniform independent and identically distributed (i.i.d.) sources, Shannon limit.Paper approved by A. K. Khandani, the Editor for Coding and Information Theory of the IEEE Communications Society.

Abstract-This work addresses the problem of designing Turbo codes for nonuniform binary memoryless or independent and identically distributed (i.i.d.) sources over noisy channels. The extrinsic information in the decoder is modified to exploit the source redundancy in the form of nonuniformity; furthermore, the constituent encoder structure is optimized for the considered nonuniform i.i.d. source to further enhance the system performance. Some constituent encoders are found to substantially outperform Berrou's (37, 21) encoder. Indeed, it is shown that the bit error rate (BER) performance of the newly designed Turbo codes is greatly improved as significant coding gains are obtained.

Abstract-We investigate the construction of joint sourcechannel (JSC) Turbo codes for the reliable communication of binary Markov sources over additive white Gaussian noise and Rayleigh fading channels. To exploit the source Markovian redundancy, the first constituent Turbo decoder is designed according to a modified version of Berrou's original decoding algorithm that employs the Gaussian assumption for the extrinsic information. Due to interleaving, the second constituent decoder is unable to adopt the same decoding method; so its extrinsic information is appropriately adjusted via a weighted correction term. The Turbo encoder is also optimized according to the Markovian source statistics and by allowing different or asymmetric constituent encoders. Simulation results demonstrate substantial gains over the original (unoptimized) Turbo codes, hence significantly reducing the performance gap to the Shannon limit. Finally, we show that our JSC coding system considerably outperforms tandem coding schemes for bit error rates smaller than 10 −4 , while enjoying a lower system complexity.Index Terms-Joint source-channel coding, turbo codes, AWGN and Rayleigh fading channels, Shannon limit, Markov sources, iterative decoding, bit error rate.

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