773 research outputs found
Polar Codes: Robustness of the Successive Cancellation Decoder with Respect to Quantization
Polar codes provably achieve the capacity of a wide array of channels under
successive decoding. This assumes infinite precision arithmetic. Given the
successive nature of the decoding algorithm, one might worry about the
sensitivity of the performance to the precision of the computation.
We show that even very coarsely quantized decoding algorithms lead to
excellent performance. More concretely, we show that under successive decoding
with an alphabet of cardinality only three, the decoder still has a threshold
and this threshold is a sizable fraction of capacity. More generally, we show
that if we are willing to transmit at a rate below capacity, then we
need only bits of precision, where is a universal
constant.Comment: In ISIT 201
Rate-Flexible Fast Polar Decoders
Polar codes have gained extensive attention during the past few years and
recently they have been selected for the next generation of wireless
communications standards (5G). Successive-cancellation-based (SC-based)
decoders, such as SC list (SCL) and SC flip (SCF), provide a reasonable error
performance for polar codes at the cost of low decoding speed. Fast SC-based
decoders, such as Fast-SSC, Fast-SSCL, and Fast-SSCF, identify the special
constituent codes in a polar code graph off-line, produce a list of operations,
store the list in memory, and feed the list to the decoder to decode the
constituent codes in order efficiently, thus increasing the decoding speed.
However, the list of operations is dependent on the code rate and as the rate
changes, a new list is produced, making fast SC-based decoders not
rate-flexible. In this paper, we propose a completely rate-flexible fast
SC-based decoder by creating the list of operations directly in hardware, with
low implementation complexity. We further propose a hardware architecture
implementing the proposed method and show that the area occupation of the
rate-flexible fast SC-based decoder in this paper is only of the total
area of the memory-based base-line decoder when 5G code rates are supported
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