THIS PAPER IS ELIGIBLE FOR THE STUDENT PAPER AWARD. Generalized integrated interleaved (GII) codes have an enhanced error-correction capability over an array of interleaves which are also known as component codes. With BCH component codes, the GII codes are called GII-BCH codes. The existing Chase decoding of GII-BCH codes can achieve a significant coding gain over hard-decision decoding of the codes, but at the cost of complexity. On the other aspect, the existing theoretical characterization of the codes' Chase decoding performance remains complex, and even partially numerical. This paper introduces a new theoretical characterization for Chase decoding performance of the codes, offering a simpler and computationally friendly closed form expression. Based on it, this paper further proposes a new Chase decoding method for GII-BCH codes, namely the enhanced Chase decoding (ECD). The ECD can identify the decoding rounds which are more likely to declare a decoding failure and prioritize allocating the flipped positions to them. Our simulation results show that with a similar maximum number of test-vectors, the ECD can achieve an improved performance over the existing Chase decoding.

Generalized integrated interleaved (GII) codes enable an enhanced error-correction over an array of interleaves (component codes) within a single block. Error-correction performance of GII codes can be further improved by utilizing the soft received information. The existing Chase decoding of GII-BCH codes can achieve a significant coding gain over the hard-decision decoding, but at the cost of complexity. Meanwhile, the existing theoretical characterization of its Chase decoding performance remains complex and partially empirical. This paper introduces a new theoretical characterization for Chase decoding performance of GII-BCH codes. With this characterization, it further proposes two new soft-decision decoding methods for GII-BCH codes, including the enhanced Chase decoding (ECD) and the enhanced concatenated Chase decoding (ECCD). They both identify the decoding rounds that are more likely to declare a decoding failure and prioritize allocating the flipped positions to those rounds. In particular, the latter utilizes codewords of a linear block code to cover the least reliable or the second least reliable positions, further improving the error-correction performance over the ECD. With a similar number of test-vectors, both the ECD and ECCD can outperform the existing Chase decoding for GII-BCH codes.

Provable security based on complexity theory provides an efficient way for providing the convincing evidences of security. In this paper, we present a definition of generic ID-based signature schemes by extending the definition of generic signature schemes, and prove the Forking lemma for that. Then we propose a new and efficient ID-based signature scheme built upon bilinear maps. We prove its security under k-CAA computational assumption in the random oracle model.