A New Class of Multiple-Rate Codes Based on Block Markov Superposition Transmission

Abstract

Hadamard transform (HT) as over the binary field provides a natural way to implement multiple-rate codes (referred to as HT-coset codes), where the code length N = 2 p is fixed but the code dimension K can be varied from 1 to N − 1 by adjusting the set of frozen bits. The HT-coset codes, including ReedMuller (RM) codes and polar codes as typical examples, can share a pair of encoder and decoder with implementation complexity of order O(N log N ). However, to guarantee that all codes with designated rates perform well, HT-coset coding usually requires a sufficiently large code length, which in turn causes difficulties in the determination of which bits are better for being frozen. In this paper, we propose to transmit short HT-coset codes in the so-called block Markov superposition transmission (BMST) manner.At the transmitter, signals are spatially coupled via superposition, resulting in long codes. At the receiver, these coupled signals are recovered by a sliding-window iterative soft successive cancellation decoding algorithm. Most importantly, the performance around or below the bit-error-rate (BER) of 10 −5 can be predicted by a simple genie-aided lower bound. Both these bounds and simulation results show that the BMST of short HT-coset codes performs well (within one dB away from the corresponding Shannon limits) in a wide range of code rates.

Performance Analysis of Block Markov Superposition Transmission of Short Codes

“…The above procedure requires no optimization and hence can be easily implemented given that the performance curve f Basic (γ b ) is available, as is the usual case for short codes. 3 Its effectiveness has been confirmed by construction examples in [16,17,27,28]. The encoding memories for some BMST codes required to approach the corresponding Shannon limits at given target BERs are shown in Table I.…”

“…To decode BMST codes, a sliding window decoding algorithm with a tunable decoding delay can be used, as with SC-LDPC codes [26]. The construction of BMST codes is flexible [27,28], in the sense that it applies to all code rates of interest in the interval (0,1). Further, BMST codes have near-capacity performance (observed by simulation) in the waterfall region of the bit-error-rate (BER) cruve and an error floor (predicted by analysis) that can be controlled by the encoding memory.…”

A Low-Complexity Delay-Tunable Coding Scheme for Visible Light Communication Systems

“…Hence, it is desirable to design codes with a variety of parameters that can share essentially the same fundamental encoder/decoder architectures. This purpose can be partially fulfilled by previously existing rate-compatible (RC) codes [10,11] and multiplerate (MR) codes [12,13]. RC codes are usually constructed from a mother code by puncturing, shortening, and/or extending [11], which usually have constant information length and different block lengths for different rates.…”

“…RC codes are usually constructed from a mother code by puncturing, shortening, and/or extending [11], which usually have constant information length and different block lengths for different rates. In contrast, MR codes [12,13] have constant block length for different rates. In this letter, we consider a new type of coding scheme, which admits essentially the same encoder/decoder hardware modules to implement a set of codes.…”

EXIT chart analysis of block markov superposition transmission of short codes

“…To decode BMST codes, a sliding window decoding algorithm with a tunable decoding delay can be used, as with SC-LDPC codes. The construction of BMST codes is flexible [17], in the sense that it applies to all code rates of interest in the interval (0,1). Further, BMST codes have near-capacity performance (observed by simulation) in the waterfall region of the bit-error-rate (BER) cruve and an error floor (predicted by analysis) that can be controlled by the encoding memory.…”