Automatic Decoder Synthesis: Methods and Case Studies

Abstract

Abstract-Upon receiving the output sequence streaming from a sequential encoder, a decoder reconstructs the corresponding input sequence that streamed to the encoder. Such an encoding and decoding scheme is commonly encountered in communication, cryptography, signal processing, and other applications. Given an encoder specification, decoder design can be errorprone and time consuming. Its automation may help designers improve productivity and justify encoder correctness. Though recent advances showed promising progress, there is still no complete method that decides whether a decoder exists for a finite state transition system. The quest for completely automatic decoder synthesis remains. This paper presents a complete and practical approach to automating decoder synthesis via incremental SAT solving and Craig interpolation. Experiments show that, for decoder-existent cases, our method synthesizes decoders effectively; for decoder-nonexistent cases, our method concludes the non-existence instantly while prior methods may fail. Case studies are also conducted in synthesizing decoders for linear error-correcting codes.

Synthesis of feedback decoders for initialized encoders

“…Circuits XGXS, Scrambler, PCIE, and T2Ethernet are from [11]; the CC series circuits are convolutional code encoders from [7,8]; circuit AD is the encoder of Figure 1; the Huff series circuits are Huffman code encoders; the LFSR series circuits correspond to linear feedback shift registers; the SBC circuit is a sliding block code encoder; others are from the MCNC and ISCAS benchmark suites. In the following experiments, the obtained decoder circuits were optimized in ABC under the script "strash; scleanup; dsd; strash; dc2; dc2; dch; map", where technology mapping was performed using the mcnc.genlib library.…”

“…In the following experiments, the obtained decoder circuits were optimized in ABC under the script "strash; scleanup; dsd; strash; dc2; dc2; dch; map", where technology mapping was performed using the mcnc.genlib library. Tables 2, 3, and 4 show the statistics of Decosy [7,8] assuming uninitialized encoder operation and our new Decosyi assuming initialized encoder operation. It should be emphasized that the two approaches cannot be directly compared as their decoding problems are fundamentally different.…”

“…That is, the decoder must causally recover a prefix of the original input sequence on-the-fly based on a so-far observed encoded sequence. Unlike prior work [11,12,7,8], the encoder under our consideration can have normal operation under non-dangling states, and the synthesized decoder can recover the original input sequence starting from the very first input (though with some time delay).…”

“…Shen et al [11] proposed a bounded decoder synthesis method with no termination guarantee. Complete synthesis methods were later established independently by Shen et al [12] and Liu et al [7,8]. Particularly, Liu et al [7,8] exploited incremental satisfiability (SAT) solving [5] and Craig interpolation [3,9,6] techniques for efficient computation.…”

“…In essence, sequential feedbacks are a necessity for such decoders. Figure 1, modified from [7,8], shows one such encoder example, whose decoder exists with respect to any initial state but does not exist if no initial state is specified. The decoding must depend on the entire input history, which is unbounded and accounts for the necessity of sequential feedbacks.…”