Spatially Coupled Repeater-Combiner-Convolutional Codes

Abstract

A form of spatially coupled codes is obtained by coupling multiple identical concatenated codes consisting of a block outer code (a repetition code followed by a single-parity code) concatenated with a convolutional inner code of infinite impulse response. The coupling operation involves only the outer code of the block-convolutional concatenated code. Because of the simple outer code and diverse inner code, the proposed codes have simple encoding implementation and flexible designation space. Extrinsic information functions are used to analyze the belief propagation (BP) thresholds of the proposed codes over an additive white Gaussian noise channel. The numerical results demonstrate that the proposed codes have better BP threshold and error correction performances than conventional spatially coupled repeat-accumulate codes and spatially coupled low-density parity-check codes. In particular, the proposed codes with a rate of about 0.5 and length of 15628 have a bit-error-rate (BER) of $10^{-5}$ at Eb/N0 of 1.13 dB that is less than 1 dB away from the Shannon limit.