Decoding of Single Parity-Check (SPC) Codes for Transmissions of Compressed Data

Abstract

This paper proposes a modification on the existing coding scheme of single parity-check (SPC) codes for compressed data. SPC codes are selected in this paper to keep high coding rate for transmissions of, for example, multimedia transmissions, where reliability should be kept high. In this paper, to improve the error correction capability, we introduce a new variable $\chi$ to exploit the source statistic in the decoding process by taking the log-likelihood ratio (LLR) of the occurrence probability of 0" and 1" of the compressed data. To verify effectiveness of the proposed modified SPC codes, we use a practical compressed data of Indonesian text being compressed with Huffman codes and also introduce extreme dummy sources having extreme inequality of appearance probability of ”0” and ”1” such that the performances with different $\chi$ values are observable. We evaluate the performance of the proposed modification on the SPC codes in terms of bit-error-rate (BER) under additive white Gaussian noise (AWGN), block Rayleigh fading, and fast Rayleigh fading channels using a series of computer simulations. The results show that the proposed modified SPC codes provide better BER performance under all channel models, where the improvement is higher if the $\chi$ value increases. The results are expected to contribute to the development of compressed data transmissions having high reliability.