On the complexity of unary error correction codes for the near-capacity transmission of symbol values from an infinite set

Unary Error Correction (UEC) codes have recently been proposed for the near-capacity Joint Source and Channel Coding (JSCC) of symbol values that are selected from a set having an infinite cardinality. In this paper, we characterize the computational complexity of UEC decoders and use complexity analysis for striking a desirable trade-off between the contradictory requirements of low complexity and near-capacity operation. We investigate a wide range of application scenarios and offer a deep insight into their beneficial parameterizations. In particular, we introduce puncturing for controlling the scheme’s throughput and for facilitating fair comparisons with a Separate Source and Channel Coding (SSCC) benchmarker. The UEC scheme is found to offer almost 1.3 dB gain, when operating within 1.6 dB of the capacity bound. This is achieved without any increase in transmission energy, bandwidth, transmit duration or decoding complexity

Adaptive iterative detection for expediting the convergence of a serially concatenated unary error correction decoder, turbo decoder and an iterative demodulator

Unary Error Correction (UEC) codes constitute a recently proposed Joint Source and Channel Code (JSCC) family, conceived for alphabets having an infinite cardinality, whilst out-performing previously used Separate Source and Channel Codes (SSCCs). UEC based schemes rely on an iterative decoding process, which involves three decoding blocks when concatenated with a turbo code. Owing to this, following the activation of one of the three blocks, the next block to be activated must be chosen from the other two decoding block options. Furthermore, the UEC decoder offers a number of decoding options, allowing its complexity and error correction capability to be dynamically adjusted. It has been shown that iterative decoding convergence can be expedited by activating the specific decoding option that offers the highest Mutual Information (MI) improvement to computational complexity ratio. This paper introduces an iterative demodulator, which is shown to improve the associated error correction performance, while reducing the overall iterative decoding complexity. The challenge is that the iterative demodulator has to forward its soft-information to the other two iterative decoding blocks, and hence the corresponding MI improvements cannot be compared on a like-for-like basis. Additionally, we also propose a method of eliminating the logarithmic calculations from the adaptive iterative decoding algorithm, hence further reducing its implementational complexity without impacting its error correcting performance