Turbo decoders which adapt to noise distribution mismatch

This article investigates the sensitivity of turbo decoder performance to mismatch of the noise distribution, and proposes a simple on-line procedure for estimating the unknown noise distribution from each block of received signal. This procedure consists of: (1) quantization of the received signal and (2) estimation of the noise distribution from the histogram of the quantized received signal. For Gaussian and Laplacian noise, the proposed procedure leads to decoder performances which are comparable (within 0.1 dB at bit-error rate of 10 ^-4) to the case where the noise distribution is known exactly     

Zigzag codes and concatenated zigzag codes

This paper introduces a family of error-correcting codes called zigzag codes. A zigzag code is described by a highly structured zigzag graph. Due to the structural properties of the graph, very low-complexity soft-in/soft-out decoding rules can be implemented. We present a decoding rule, based on the Max-Log-APP (MLA) formulation, which requires a total of only 20 addition-equivalent operations per information bit, per iteration. Simulation of a rate-1/2 concatenated zigzag code with four constituent encoders with interleaver length 65 536, yields a bit error rate (BER) of 10^-5 at 0.9 dB and 1.3 dB away from the Shannon limit by optimal (APP) and low-cost suboptimal (MLA) decoders, respectively. A union bound analysis of the bit error probability of the zigzag code is presented. It is shown that the union bounds for these codes can be generated very efficiently. It is also illustrated that, for a fixed interleaver size, the concatenated code has increased code potential as the number of constituent encoders increases. Finally, the analysis shows that zigzag codes with four or more constituent encoders have lower error floors than comparable turbo codes with two constituent encoders     

Duality theorems for joint source-channel coding

We consider joint source-channel coding for a memoryless Gaussian source and an additive white Gaussian noise (AWGN) channel. For a given code defined by an encoder-decoder pair (α, β), its dual code is obtained by interchanging the encoder and decoder: (β, α). It is shown that if a code (α, β) is optimal at rate p channel uses per source sample and if it satisfies a certain uniform continuity condition, then its dual code (β, α) is optimal for rate 1/ρ channel uses per source sample. Further, it is demonstrated that there is a code which is optimal but its dual code is not optimal. Finally, using random coding, we show that there is an optimal code which has an optimal dual. The duality concept is also presented for the cases of (i) binary memoryless equiprobable source and binary-symmetric channel (BSC), and (ii) colored Gaussian source and additive colored Gaussian noise (ACGN) channel